Ramm A.G. Dynamical systems method and applications: theoretical developments and numerical examples / A.G.Ramm, N.S.Hoang. - Hoboken: Wiley, 2012. - xxix, 539 p.: ill., charts. - Ref.: p.525-535. - Ind.: p.537-539. - ISBN 978-1-118-02428-7  Место хранения:   070 | Институт систем энергетики им. Л.А.Мелентьева CO РАН | Иркутск | Библиотека

Оглавление / Contents

PART I 1 Introduction ................................................. 3 2 Ill-posed problems .......................................... 11 3 DSM for well-posed problems ................................. 57 4 DSM and linear ill-posed problems ........................... 71 5 Some inequalities ........................................... 93 6 DSM for monotone operators ................................. 133 7 DSM for general nonlinear operator equations ............... 145 8 DSM for operators satisfying a spectral assumption ......... 155 9 DSM in Banach spaces ....................................... 161 10 DSM and Newton-type methods without inversion of the derivative ................................................. 169 11 DSM and unbounded operators ................................ 177 12 DSM and nonsmooth operators ................................ 181 13 DSM as a theoretical tool .................................. 195 14 DSM and iterative methods .................................. 201 15 Numerical problems arising in applications ................. 213 PART II 16 Solving linear operator equations by a Newton-type DSM ..... 255 17 DSM of gradient type for solving linear operator equations .................................................. 269 18 DSM for solving linear equations with finite-rank operators .................................................. 281 19 A discrepancy principle for equations with monotone continuous operators ....................................... 295 20 DSM of Newton-type for solving operator equations with minimal smoothness assumptions ............................. 307 21 DSM of gradient type ....................................... 347 22 DSM of simple iteration type ............................... 373 23 DSM for solving nonlinear operator equations in Banach spaces ..................................................... 409 PART III 24 Solving linear operator equations by the DSM ............... 423 25 Stable solutions of Hammerstein-type integral equations .... 441 26 Inversion of the Laplace transform from the real axis using an adaptive iterative method ......................... 455