Lau H.T. A numerical library in Java for scientists and engineers
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Lau H.T. A numerical library in Java for scientists and engineers / Lau H.T. - Boca Raton: Chapman & Hall/CRC, 2004. - 1063 p. + 1 CD-ROM. - ISBN 1-58488-430-4.
 
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  INTRODUCTION ..................................... 1

  1. ELEMENTARY PROCEDURES ......................... 3

  1.1 Real vector and matrix — Initialization ............................ 3
       A. inivec ......................................................... 3
       B. inimat ......................................................... 3
       C. inimatd ........................................................ 4
       D. inisymd ........................................................ 4
       E. inisymrow ...................................................... 5

  1.2 Real vector and matrix — Duplication ............................... 6
       A. dupvec ......................................................... 6
       B. dupvecrow ...................................................... 6
       C. duprowvec ...................................................... 7
       D. dupveccol ...................................................... 7
       E. dupcolvec ...................................................... 7
       F. dupmat ......................................................... 8

  1.3 Real vector and matrix — Multiplication ............................ 8
       A. mulvec ......................................................... 8
       B. mulrow ......................................................... 9
       C. mulcol ......................................................... 9
       D. colcst ........................................................ 10
       E. rowcst ........................................................ 10

  1.4 Real vector vector products ....................................... 10
       A. vecvec ........................................................ 10
       B. matvec ........................................................ 11
       C. tamvec ........................................................ 12
       D. matmat ........................................................ 12
       E. tammat ........................................................ 13
       F. mattam ........................................................ 13
       G. seqvec ........................................................ 14
       H. scaprdl ....................................................... 14
       I. symmatvec ..................................................... 15

  1.5 Real matrix vector products ....................................... 16
       A. fulmatvec ..................................................... 16
       B. fultamvec ..................................................... 16
       C. fulsymmatvec .................................................. 17
       D. resvec ........................................................ 17
       E. symresvec ..................................................... 18

  1.6 Real matrix matrix products ....................................... 18
       A. hshvecmat ..................................................... 18
       B. hshcolmat ..................................................... 19
       C. hshrowmat ..................................................... 20
       D. hshvectam ..................................................... 20
       E. hshcoltam ..................................................... 21
       F. hshrowtam ..................................................... 21

  1.7 Real vector and matrix — Elimination .............................. 22
       A. elmvec ........................................................ 22
       B. elmcol ........................................................ 22
       C. elmrow ........................................................ 23
       D. elmveccol ..................................................... 23
       E. elmcolvec ..................................................... 23
       F. elmvecrow ..................................................... 24
       G. elmrowvec ..................................................... 24
       H. elmcolrow ..................................................... 25
       I. elmrowcol ..................................................... 25
       J. maxelmrow ..................................................... 26

  1.8 Real vector and matrix—Interchanging .............................. 26
       A. ichvec ........................................................ 26
       B. ichcol ........................................................ 27
       C. ichrow ........................................................ 27
       D. ichrowcol ..................................................... 28
       E. ichseqvec ..................................................... 29
       F. ichseq ........................................................ 29

  1.9 Real vector and matrix — Rotation ................................. 30
       A. rotcol ........................................................ 30
       B. rotrow ........................................................ 30

  1.10 Real vector and matrix — Norms ................................... 31
       A. infnrmvec ..................................................... 31
       B. infnrmrow ..................................................... 32
       C. infhrmcol ..................................................... 32
       D. infnrmmat ..................................................... 33
       E. onenrmvec ..................................................... 34
       F. onenrmrow ..................................................... 34
       G. onenrmcol ..................................................... 35
       H. onenrmmat ..................................................... 36
       I. absmaxmat ..................................................... 36

  1.11 Real vector and matrix — Scaling ................................. 37
     reascl ............................................................. 37

  1.12 Complex vector and matrix — Multiplication ....................... 38
       A. comcolcst ..................................................... 38
       B. comrowcst ..................................................... 39

  1.13 Complex vector and matrix — Scalar products ...................... 40
       A. commatvec ..................................................... 40
       B. hshcomcol ..................................................... 40
       C. hshcomprd ..................................................... 42

  1.14 Complex vector and matrix — Elimination .......................... 43
       A. elmcomveccol .................................................. 43
       B. elmcomcol ..................................................... 44
       C. elmcomrowvec .................................................. 44

  1.15 Complex vector and matrix — Rotation ............................. 45
       A. rotcomcol ..................................................... 45
       B. rotcomrow ..................................................... 46
       C. chsh2 ......................................................... 47

  1.16 Complex vector and matrix—Norms .................................. 48
     comeucnrm .......................................................... 48

  1.17 Complex vector and matrix — Scaling .............................. 48
       A. comscl ........................................................ 48
       B. sclcom ........................................................ 50

  1.18 Complex monadic operations ....................................... 51
       A. comabs ........................................................ 51
       B. comsqrt ....................................................... 51
       C. carpol ........................................................ 53

  1.19 Complex dyadic operations ........................................ 53
       A. commul ........................................................ 53
       B. comdiv ........................................................ 54

  1.20 Long integer arithmetic .......................................... 55
       A. lngintadd ..................................................... 55
       B. lngintsubtract ................................................ 56
       C. lngintmult .................................................... 58
       D. lngintdivide .................................................. 59
       E. lngintpower ................................................... 62

  2. ALGEBRAIC EVALUATIONS ........................ 64

  2.1 Evaluation of polynomials in Grunert form ......................... 64
       A. pol ........................................................... 64
       B. taypol ........................................................ 65
       C. norderpol ..................................................... 66
       D. derpol ........................................................ 66

  2.2 Evaluation of general orthogonal polynomials ...................... 67
       A. ortpol ........................................................ 67
       B. ortpolsym ..................................................... 68
       C. allortpol ..................................................... 69
       D. allortpolsym .................................................. 70
       E. sumortpol ..................................................... 70
       F. sumortpolsym .................................................. 71

  2.3 Evaluation of Chebyshev polynomials ............................... 72
       A. chepolsum ..................................................... 72
       B. oddchepolsum .................................................. 73
       C. chepol ........................................................ 74
       D. allchepol ..................................................... 74

  2.4 Evaluation of Fourier series ...................................... 75
       A. sinser ........................................................ 75
       B. cosser ........................................................ 77
       C. fouser ........................................................ 78
       D. fouser1 ....................................................... 79
       E. fbuser2 ....................................................... 80
       F. comfouser ..................................................... 80
       G. comfouser1 .................................................... 82
       H. comfouser2 .................................................... 83

  2.5 Evaluation of continued fractions ................................. 84
     jfrac .............................................................. 84

  2.6 Transformation of polynomial representation ....................... 85
       A. polchs ........................................................ 85
       B. chspol ........................................................ 86
       C. polshtchs ..................................................... 86
       D. shtchspol ..................................................... 87
       E. grnnew ........................................................ 87
       F. newgrn ........................................................ 88
       G. lintfmpol ..................................................... 89

  2.7 Operations on orthogonal polynomials .............................. 90
     intchs ............................................................. 90

  3. LINEAR ALGEBRA ............................... 92

  3.1 Full real general matrices ........................................ 92
     3.1.1 Preparatory procedures ....................................... 92
       A. dec ........................................................... 92
       B. gsselm ........................................................ 94
       C. onenrminv ..................................................... 97
       D. erbelm ........................................................ 98
       E. gsserb ........................................................ 99
       F. gssnri ....................................................... 100
     3.1.2 Calculation of determinant .................................. 101
       determ .......................................................... 101
     3.1.3 Solution of linear equations ................................ 101
       A. sol .......................................................... 101
       B. decsol ....................................................... 102
       C. solelm ....................................................... 103
       D. gsssol ....................................................... 104
       E. gsssolerb .................................................... 105
     3.1.4 Matrix inversion ............................................ 106
       A. inv .......................................................... 106
       B. decinv ....................................................... 107
       C. inv1 ......................................................... 108
       D. gssinv ....................................................... 109
       E. gssinverb .................................................... 109
     3.1.5 Iteratively improved solution ............................... 111
       A. itisol ....................................................... 111
       B. gssitisol .................................................... 113
       C. itisolerb .................................................... 114
       D. gssitisolerb ................................................. 116

  3.2 Real symmetric positive definite matrices ........................ 118
     3.2.1 Preparatory procedures ...................................... 118
       A. chldec2 ...................................................... 118
       B. chldec1 ...................................................... 119
     3.2.2 Calculation of determinant .................................. 120
       A. chldeterm2 ................................................... 120
       B. chldeterm1 ................................................... 121
     3.2.3 Solution of linear equations ................................ 121
       A. chlsol2 ...................................................... 121
       B. chlsol1 ...................................................... 122
       C. chldecsol2 ................................................... 123
       D. chldecsol1 ................................................... 124
     3.2.4 Matrix inversion ............................................ 125
       A. chlinv2 ...................................................... 125
       B. chlinv1 ...................................................... 125
       C. chldecinv2 ................................................... 126
       D. chldecinv1 ................................................... 127

  3.3 General real symmetric matrices .................................. 128
     3.3.1 Preparatory procedure ....................................... 128
       decsym2 ......................................................... 128
     3.3.2 Calculation of determinant .................................. 133
       determsym2 ...................................................... 133
     3.3.3 Solution of linear equations ................................ 133
       A. solsym2 ...................................................... 133
       B. decsolsym2 ................................................... 135

  3.4 Real full rank overdetermined systems ............................ 136
     3.4.1 Preparatory procedures ...................................... 136
       A. Isqortdec .................................................... 136
       B. Isqdglinv .................................................... 138
     3.4.2 Least squares solution ...................................... 139
       A. Isqsol ....................................................... 139
       B. Isqortdecsol ................................................. 140
     3.4.3 Inverse matrix of normal equations .......................... 141
       Isqinv .......................................................... 141
     3.4.4 Least squares with linear constraints ....................... 142
       A. Isqdecomp .................................................... 142
       B. Isqrefsol .................................................... 146

  3.5 Other real matrix problems ....................................... 149
     3.5.1 Solution of overdetermined systems .......................... 149
       A. solsvdovr .................................................... 149
       B. solovr ....................................................... 151
     3.5.2 Solution of underdetermined systems ......................... 152
       A. solsvdund .................................................... 152
       B. solund ....................................................... 153
     3.5.3 Solution of homogeneous equation ............................ 154
       A. homsolsvd .................................................... 154
       B. homsol ....................................................... 155
     3.5.4 Pseudo-inversion ............................................ 156
       A. psdinvsvd .................................................... 156
       B. psdinv ....................................................... 157

  3.6 Real sparse nonsymmetric band matrices ........................... 158
     3.6.1 Preparatory procedure ....................................... 158
       decbnd .......................................................... 158
     3.6.2 Calculation of determinant .................................. 161
       determbnd ....................................................... 161
     3.6.3 Solution of linear equations ................................ 162
       A. solbnd ....................................................... 162
       B. decsolbnd .................................................... 163

  3.7 Real sparse nonsymmetric tridiagonal matrices .................... 166
     3.7.1 Preparatory procedures ...................................... 166
       A. dectri ....................................................... 166
       B. dectripiv .................................................... 167
     3.7.2 Solution of linear equations ................................ 170
       A. soltri ....................................................... 170
       B. decsoltri .................................................... 171
       C. soltripiv .................................................... 172
       D. decsoltripiv ................................................. 173

  3.8 Sparse symmetric positive definite band matrices ................. 176
     3.8.1 Preparatory procedure ....................................... 176
       chldecbnd ....................................................... 176
     3.8.2 Calculation of determinant .................................. 178
       chldetermbnd .................................................... 178
     3.8.3 Solution of linear equations ................................ 179
       A. chlsolbnd .................................................... 179
       B. chldecsolbnd ................................................. 180

  3.9 Symmetric positive definite tridiagonal matrices ................. 180
     3.9.1 Preparatory procedure ....................................... 180
       decsymtri ....................................................... 180
     3.9.2 Solution of linear equations ................................ 182
       A. solsymtri .................................................... 182
       B. decsolsymtri ................................................. 183

  3.10 Sparse real matrices — Iterative methods ........................ 184
       conjgrad ........................................................ 184

  3.11 Similarity transformation ....................................... 186
     3.11.1 Equilibration - real matrices .............................. 186
       A. eqilbr ....................................................... 186
       B. baklbr ....................................................... 188
     3.11.2 Equilibration - complex matrices ........................... 189
       A. eqilbrcom .................................................... 189
       B. baklbrcom .................................................... 192
     3.11.3 To Hessenberg form - real symmetric ........................ 192
       A. tfmsymtri2 ................................................... 192
       B. baksymtri2 ................................................... 194
       C. tfmprevec .................................................... 195
       D. tfmsymtri1 ................................................... 196
       E. baksymtri1 ................................................... 198
     3.11.4 To Hessenberg form - real asymmetric ....................... 199
       A. tfmreahes .................................................... 199
       B. bakreahes1 ................................................... 200
       C. bakreahes2 ................................................... 201
     3.11.5 To Hessenberg form- complex Hermitian ...................... 202
       A. hshhrmtri .................................................... 202
       B. hshhrmtrival ................................................. 205
       C. bakhrmtri .................................................... 207
     3.11.6 To Hessenberg form — Complex non-Hermitian ................. 208
       A. hshcomhes .................................................... 208
       B. bakcomhes .................................................... 210

  3.12 Other transformations ........................................... 212
     3.12.1 To bidiagonal form - real matrices ......................... 212
       A. hshreabid .................................................... 212
       B. psttfmmat .................................................... 214
       C. pretfmmat .................................................... 214

  3.13 The (ordinary) eigenvalue problem ............................... 215
     3.13.1 Real symmetric tridiagonal matrices ........................ 215
       A. valsymtri .................................................... 215
       B. vecsymtri .................................................... 219
       C. qrivalsymtri ................................................. 223
       D. qrisymtri .................................................... 225
     3.13.2 Real symmetric full matrices ............................... 228
       A. eigvalsym2 ................................................... 228
       B. eigsym2 ...................................................... 229
       C. eigvalsym1 ................................................... 230
       D. eigsym1 ...................................................... 231
       E. qrivalsym2 ................................................... 233
       F. qrisym ....................................................... 234
       G. qrivalsym1 ................................................... 234
     3.13.3 Symmetric matrices - Auxiliary procedures .................. 235
       A. mergesort .................................................... 235
       B. vecperm ...................................................... 237
       C. rowperm ...................................................... 238
     3.13.4 Symmetric matrices - Orthogonalization ..................... 239
       orthog .......................................................... 239
     3.13.5 Symmetric matrices - Iterative improvement ................. 240
       symeigimp ....................................................... 240
     3.13.6 Asymmetric matrices in Hessenberg form ..................... 244
       A. reavalqri .................................................... 244
       B. reaveches .................................................... 246
       C. reaqri ....................................................... 249
       D. comvalqri .................................................... 252
       E. comveches .................................................... 255
     3.13.7 Real asymmetric full matrices .............................. 258
       A. reaeigval .................................................... 258
       B. reaeig1 ...................................................... 259
       C. reaeig3 ...................................................... 262
       D. comeigval .................................................... 263
       E. comeig1 ...................................................... 264
     3.13.8 Complex Hermitian matrices ................................. 267
       A. eigvalhrm .................................................... 267
       B. eighrm ....................................................... 268
       C. qrivalhrm .................................................... 270
       D. qrihrm ....................................................... 271
     3.13.9 Complex upper-Hessenberg matrices .......................... 272
       A. valqricom .................................................... 272
       B. qricom ....................................................... 275
     3.13.10 Complex full matrices ..................................... 280
       A. eigvalcom .................................................... 280
       B. eigcom ....................................................... 281

  3.14 The generalized eigenvalue problem .............................. 283
     3.14.1 Real asymmetric matrices ................................... 283
       A. qzival ....................................................... 283
       B. qzi .......................................................... 289
       C. hshdecmul .................................................... 298
       D. hestgl3 ...................................................... 299
       E. hestgl2 ...................................................... 300
       F. hsh2col ...................................................... 301
       G. hsh3col ...................................................... 302
       H. hsh2row3 ..................................................... 304
       I. hsh2row2 ..................................................... 305
       J. hsh3row3 ..................................................... 307
       K. hsh3row2 ..................................................... 308

  3.15 Singular values ................................................. 310
     3.15.1 Real bidiagonal matrices ................................... 310
       A. qrisngvalbid ................................................. 310
       B. qrisngvaldecbid .............................................. 312
     3.15.2 Real full matrices ......................................... 315
       A. qrisngval .................................................... 315
       B. qrisngvaldec ................................................. 316

  3.16 Zeros of polynomials ............................................ 318
     3.16.1 Zeros of general real polynomials .......................... 318
       A. zerpol ....................................................... 318
       B. bounds ....................................................... 325
     3.16.2 Zeros of orthogonal polynomials ............................ 331
       A. allzerortpol ................................................. 331
       B. lupzerortpol ................................................. 332
       C. selzerortpol ................................................. 335
       D. alljaczer .................................................... 336
       E. alllagzer .................................................... 338
     3.16.3 Zeros of complex polynomials ............................... 339
       comkwd .......................................................... 339

  4. ANALYTIC EVALUATIONS ........................ 341

  4.1 Evaluation of an infinite series ................................. 341
       A. euler ........................................................ 341
       B. sumposseries ................................................. 342

  4.2 Quadrature ....................................................... 349
     4.2.1 One-dimensional quadrature .................................. 349
       A. qadrat ....................................................... 349
       B. integral ..................................................... 352
     4.2.2 Multidimensional quadrature ................................. 357
       tricub .......................................................... 357
     4.2.3 Gaussian quadrature - General weights ....................... 361
       A. reccof ....................................................... 361
       B. gsswts ....................................................... 363
       C. gsswtssym .................................................... 364
     4.2.4 Gaussian quadrature - Special weights ....................... 366
       A. gssjacwghts .................................................. 366
       B. gsslagwghts .................................................. 368

  4.3 Numerical differentiation ........................................ 369
     4.3.1 Calculation with difference formulas ........................ 369
       A. jacobnnf ..................................................... 369
       B. jacobnmf ..................................................... 371
       C. jacobnbndf ................................................... 372

  5. ANALYTIC PROBLEMS ........................... 374

  5.1 Nonlinear equations .............................................. 374
     5.1.1 Single equation - No derivative available ................... 374
       A. zeroin ....................................................... 374
       B. zeroinrat .................................................... 377
     5.1.2 Single equation - Derivative available ...................... 380
       zeroinder ....................................................... 380
     5.1.3 System of equations - No Jacobian matrix .................... 383
       A. quanewbnd .................................................... 383
       B. quanewbnd1 ................................................... 387

  5.2 Unconstrained optimization ....................................... 389
     5.2.1 One variable -No derivative ................................. 389
       minin ........................................................... 389
     5.2.2 One variable - Derivative available ......................... 393
       mininder ........................................................ 393
     5.2.3 More variables - Auxiliary procedures ....................... 396
       A. linemin ...................................................... 396
       B. rnk1upd ...................................................... 399
       C. davupd ....................................................... 400
       D. fleupd ....................................................... 401
     5.2.4 More variables - No derivatives ............................. 402
       praxis .......................................................... 402
     5.2.5 More variables - Gradient available ......................... 411
       A. rnk1min ...................................................... 411
       B. flemin ....................................................... 418

  5.3 Overdetermined nonlinear systems ................................. 422
     5.3.1 Least squares - With Jacobian matrix ........................ 422
       A. marquardt .................................................... 422
       B. gssnewton .................................................... 427

  5.4 Differential equations — Initial value problems .................. 433
     5.4.1 First order - No derivatives right hand side ................ 433
       A. rk1 .......................................................... 433
       B. rke .......................................................... 436
       C. rk4a ......................................................... 440
       D. rk4na ........................................................ 448
       E. rk5na ........................................................ 455
       F. multistep .................................................... 461
       G. diffsys ...................................................... 473
       H. ark .......................................................... 477
       I. efrk ......................................................... 483
     5.4.2 First order - Jacobian matrix available ..................... 492
       A. efsirk ....................................................... 492
       B. eferk ........................................................ 497
       C. liniger1vs ................................................... 504
       D. Iiniger2 ..................................................... 511
       E. gms .......................................................... 517
       F. impex ........................................................ 526
     5.4.3 First order - Several derivatives available ................. 539
       A. modifiedtaylor ............................................... 539
       B. eft .......................................................... 545
     5.4.4 Second order - No derivatives right hand side ............... 555
       A. rk2 .......................................................... 555
       B. rk2n ......................................................... 559
       C. rk3 .......................................................... 564
       D. rk3n ......................................................... 567
     5.4.5 Initial boundary value problem .............................. 572
       arkmat .......................................................... 572

  5.5 Two point boundary value problems ................................ 576
    5.5.1 Linear methods - Second order self adjoint ................... 576
       A. femlagsym .................................................... 576
       B. femlag ....................................................... 584
       C. femlagspher .................................................. 589
     5.5.2 Linear methods - Second order skew adjoint .................. 595
       femlagskew ...................................................... 595
     5.5.3 Linear methods - Fourth order self adjoint .................. 601
       femhermsym ...................................................... 601
     5.5.4 Nonlinear methods ........................................... 612
       nonlinfemlagskew ................................................ 612

  5.6 Two-dimensional boundary value problems .......................... 617
     5.6.1 Elliptic special linear systems ............................. 617
       A. richardson ................................................... 617
       B. elimination .................................................. 621

  5.7 Parameter estimation in differential equations ................... 627
    5.7.1 Initial value problems ....................................... 627
       peide ........................................................... 627

  6. SPECIAL FUNCTIONS ........................... 651
  6.1 Elementary functions ............................................. 651
     6.1.1 Hyperbolic functions ........................................ 651
       A. arcsinh ...................................................... 651
       B. arccosh ...................................................... 652
       C. arctanh ...................................................... 652
     6.1.2 Logarithmic functions ....................................... 653
       logoneplusx ..................................................... 653

  6.2 Exponential integral ............................................. 654
     6.2.1 Exponential integral ........................................ 654
       A. ei ........................................................... 654
       B. eialpha ...................................................... 657
       C. enx .......................................................... 657
       D. nonexpenx .................................................... 659
     6.2.2 Sine and cosine integral .................................... 661
       A. sincosint .................................................... 661
       B. sincosfg ..................................................... 662

  6.3 Gamma function ................................................... 664
       A. recipgamma ................................................... 664
       B. gamma ........................................................ 665
       C. loggamma ..................................................... 667
       D. incomgam ..................................................... 668
       E. incbeta ...................................................... 671
       F. ibpplusn ..................................................... 672
       G. ibqplusn ..................................................... 673
       H. ixqfix ....................................................... 674
       I. ixpfix ....................................................... 675
       J. forward ...................................................... 676
       K. backward ..................................................... 676

  6.4 Error function ................................................... 677
       A. errorfunction ................................................ 677
       B. nonexperfc ................................................... 678
       C. inverseerrorfunction ......................................... 680
       D. fresnel ...................................................... 682
       E. fg ........................................................... 684

  6.5 Bessel functions of integer order ................................ 686
     6.5.1 Bessel functions J and Y .................................... 686
       A. bessj0 ....................................................... 686
       B. bessj1 ....................................................... 688
       C. bessj ........................................................ 689
       D. bessy01 ...................................................... 691
       E. bessy ........................................................ 692
       F. besspq0 ...................................................... 693
       G. besspql ...................................................... 695
     6.5.2 Bessel functions I and K .................................... 696
       A. bessi0 ....................................................... 696
       B. bessi1 ....................................................... 697
       C. bessi ........................................................ 698
       D. bessk01 ...................................................... 699
       E. bessk ........................................................ 700
       F. nonexpbessi0 ................................................. 701
       G. nonexpbessi1 ................................................. 702
       H. nonexpbessi .................................................. 704
       I. nonexpbessk01 ................................................ 705
       J. nonexpbessk .................................................. 707

  6.6 Bessel functions of real order ................................... 708
     6.6.1 Bessel functions J and Y .................................... 708
       A. bessjaplusn .................................................. 708
       B. bessya01 ..................................................... 709
       C. bessyaplusn .................................................. 712
       D. besspqa01 .................................................... 713
       E. besszeros .................................................... 716
       F. start ........................................................ 719
     6.6.2 Bessel functions I and K .................................... 721
       A. bessiaplusn .................................................. 721
       B. besska01 ..................................................... 722
       C. besskaplusn .................................................. 724
       D. nonexpbessiaplusn ............................................ 725
       E. nonexpbesska01 ............................................... 726
       F. nonexpbesskaplusn ............................................ 728
     6.6.3 Spherical Bessel functions .................................. 729
       A. spherbessj ................................................... 729
       B. spherbessy ................................................... 730
       C. spherbessi ................................................... 731
       D. spherbessk ................................................... 731
       E. nonexpspherbessi ............................................. 732
       F. nonexpspherbessk ............................................. 733
     6.6.4 Airy functions .............................................. 734
       A. airy ......................................................... 734
       B. airyzeros .................................................... 738

  7. INTERPOLATION AND APPROXIMATION ............. 741

  7.1 Real data in one dimension ....................................... 741
     7.1.1 Interpolation with general polynomials ...................... 741
       newton .......................................................... 741
     7.1.2 Approximation in infinity norm .............................. 742
       A. ini .......................................................... 742
       B. sndremez ..................................................... 743
       C. minmaxpol .................................................... 746

  ADDENDA ........................................ 749

  I. Fast Fourier transforms ........................................... 749
     A. cfftp .......................................................... 749
     B. orderf ......................................................... 762
     C. cfft2p ......................................................... 764
     D. cfft2r ......................................................... 767
     E. Test_cfftp ..................................................... 772
     F. rfftr .......................................................... 776
     G. Test_rfftr ..................................................... 778

  II. Time series analysis ............................................. 780
     A. powsp .......................................................... 780
     B. Test_powsp ..................................................... 784
     C. timser ......................................................... 786
     D. Test_timser .................................................... 789
     E. timspc ......................................................... 790
     F. Test_timspc .................................................... 799

  WORKED EXAMPLES ................................ 804

  Examples for chapter 1 procedures .................................... 804
     hshcomcol, hshcomprd .............................................. 804
     elmcomcol ......................................................... 805
     rotcomcol ......................................................... 806
     comabs ............................................................ 807
     comsqrt ........................................................... 807
     carpol ............................................................ 808
     commul ............................................................ 808
     comdiv ............................................................ 809
     Ingintadd, Ingintsbtract, Ingintmult, lngintdivide, lngintpower ... 810

  Examples for chapter 2 procedures .................................... 811
     derpol ............................................................ 811
     allortpol ......................................................... 812
     chepolsum ......................................................... 812
     oddchepolsum ...................................................... 813
     chepol, allchepol ................................................. 814
     fouser ............................................................ 815
     jfrac ............................................................. 815
     chspol, polchs .................................................... 816
     polshtchs, shtchspol .............................................. 817
     newgrn, grnnew .................................................... 818
     lintfmpol ......................................................... 818
     intchs ............................................................ 819

  Examples for chapter 3 procedures .................................... 820
     determ, gsselm .................................................... 820
     decsol ............................................................ 821
     gsssol ............................................................ 822
     gsssolerb ......................................................... 823
     decinv ............................................................ 824
     gssinv ............................................................ 825
     gssinverb ......................................................... 826
     gssitisol ......................................................... 827
     gssitisolerb ...................................................... 828
     chldec2, chlsol2, chlinv2 ......................................... 829
     chldec1, chlsol1, chlinv1 ......................................... 831
     chldecsol2, chldeterm2,  chldecinv2 ............................... 832
     chldecsol1, chldeterm1, chldecinv1 ................................ 833
     determsym2 ........................................................ 835
     decsolsym2 ........................................................ 836
     lsqortdec, lsqsol, lsqdglinv ...................................... 838
     lsqortdecsol ...................................................... 839
     lsqinv ............................................................ 841
     lsqdecomp, lsqrefsol .............................................. 842
     solovr ............................................................ 844
     solund ............................................................ 845
     homsol ............................................................ 847
     psdinv ............................................................ 849
     solbnd, decbnd, determbnd ......................................... 850
     decsolbnd ......................................................... 851
     decsoltri ......................................................... 852
     soltripiv ......................................................... 853
     decsoltripiv ...................................................... 854
     chlsolbnd, chldecbnd, chldetermbnd ................................ 855
     chldecsolbnd, chldetermbnd ........................................ 856
     decsolsymtri ...................................................... 857
     conjgrad .......................................................... 858
     eqilbrcom ......................................................... 860
     hshhrmtri ......................................................... 861
     valsymtri, vecsymtri .............................................. 862
     eigsyml ........................................................... 863
     symeigimp ......................................................... 865
     comvalqri, comveches .............................................. 866
     reaeig3 ........................................................... 868
     eighrm ............................................................ 869
     qrihrm ............................................................ 871
     valqricom ......................................................... 872
     qricom ............................................................ 874
     eigcom ............................................................ 875
     qzival ............................................................ 877
     qzi ............................................................... 878
     qrisngvaldec ...................................................... 880
     zerpol, bounds .................................................... 881
     allzerortpol ...................................................... 883
     lupzerortpol ...................................................... 884
     selzerortpol ...................................................... 885
     alljaczer ......................................................... 886
     alllagzer ......................................................... 887
     comkwd ............................................................ 887

  Examples for chapter 4 procedures .................................... 888
     euler ............................................................. 888
     sumposseries ...................................................... 889
     qadrat ............................................................ 890
     integral .......................................................... 890
     tricub ............................................................ 892
     reccof ............................................................ 893
     gsswtssym ......................................................... 894
     gssjacwghts ....................................................... 895
     gsslagwghts ....................................................... 895
     jacobnnf .......................................................... 896
     jacobnmf .......................................................... 897
     jacobnbndf ........................................................ 899

  Examples for chapter 5 procedures .................................... 900
     zeroin ............................................................ 900
     zeroinrat ......................................................... 901
     zeroinder ......................................................... 902
     quanewbnd1 ........................................................ 903
     minin ............................................................. 904
     mininder .......................................................... 906
     praxis ............................................................ 907
     rnk1min, flemin ................................................... 908
     marquardt ......................................................... 910
     gssnewton ......................................................... 912
     rkl ............................................................... 914
     rke ............................................................... 915
     rk4a .............................................................. 917
     rk4na ............................................................. 918
     rk5na ............................................................. 920
     multistep ......................................................... 921
     diffsys ........................................................... 923
     ark ............................................................... 925
     efrk .............................................................. 928
     eisirk ............................................................ 930
     eferk ............................................................. 932
     liniger1vs ........................................................ 934
     liniger2 .......................................................... 936
     gms ............................................................... 940
     impex ............................................................. 942
     modifiedtaylor .................................................... 945
     eft ............................................................... 948
     rk2 ............................................................... 952
     rk2n .............................................................. 953
     rk3 ............................................................... 955
     rk3n .............................................................. 956
     arkmat ............................................................ 958
     femlagsym ......................................................... 961
     femlag ............................................................ 963
     femlagspher ....................................................... 964
     femlagskew ........................................................ 966
     femhermsym ........................................................ 968
     nonlinfemlagskew .................................................. 970
     richardson ........................................................ 972
     elimination ....................................................... 974
     peide ............................................................. 976

   Examples for chapter 6 procedures ................................... 984
     ei ................................................................ 984
     eialpha ........................................................... 984
     enx, nonexpenx .................................................... 985
     sincosint, sincosfg ............................................... 986
     recipgamma ........................................................ 987
     gamma ............................................................. 988
     loggamma .......................................................... 989
     incomgam .......................................................... 989
     incbeta ........................................................... 990
     ibpplusn .......................................................... 991
     ibqplusn .......................................................... 991
     errorfunction, nonexperfc ......................................... 992
     inverseerrorfunction .............................................. 993
     fresnel, fg ....................................................... 994
     bessj0, bessj1, bessj ............................................. 995
     bessy01 ........................................................... 995
     bessy ............................................................. 996
     besspq0, besspq1 .................................................. 997
     bessi, bessk ...................................................... 998
     bessk01 ........................................................... 999
     nonexpbessk01 .................................................... 1000
     nonexpbessk ...................................................... 1001
     bessjaplusn ...................................................... 1001
     besspqa01 ........................................................ 1002
     besszeros ........................................................ 1003
     spherbessi, nonexpspherbessi ..................................... 1004
     spherbessk, nonexpspherbessk ..................................... 1005
     airy ............................................................. 1006
     airyzeros ........................................................ 1007

   Examples for chapter 7 procedures .................................. 1007
     newton ........................................................... 1007
     ini .............................................................. 1008
     sndremez ......................................................... 1009
     minmaxpol ........................................................ 1010

   APPENDIX A: REFERENCES ....................... 1012

   APPENDIX B: PROCEDURES DESCRIPTION ........... 1021

   INDEX OF PROCEDURES .......................... 1055


Вверх Lau H.T. A numerical library in Java for scientists and engineers / Lau H.T. - Boca Raton: Chapman & Hall/CRC, 2004. - 1063 p. + 1 CD-ROM. - ISBN 1-58488-430-4.

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