Dynamical Systems Method and Applications Theoretical Developments and Numerical Examples

Name: Dynamical Systems Method and Applications Theoretical Developments and Numerical Examples
Price: 43.5 USD
Availability: InStock
ISBN: 9781118024287

ISBN-10: 1118024281

ISBN-13: 9781118024287

Edition: 2012

Authors: Alexander G. Ramm, Nguyen S. Hoang

List price: $290.95

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Description:

Dynamical Systems Method (DSM) is a powerful general method for solving operator equations. These equations can be linear or nonlinear or well-posed or ill-posed. The book presents a systematic development of the DSM, and theoretical results are illustrated by a number of numerical examples, which are of independent interest. These include: stable differentiation of noisy data, stable solution of ill-conditioned linear algebraic systems, stable solution of Fredholm and Volterra integral equations of the first kind, stable inversion of the Laplace transform from the real axis, solution of nonlinear integral equations, and other examples. Chapter coverage includes ill-posed…

Book details

List price: $290.95
Copyright year: 2012
Publisher: John Wiley & Sons, Limited
Publication date: 12/2/2011
Binding: Hardcover
Pages: 576
Size: 6.50" wide x 9.30" long x 1.30" tall
Weight: 2.090
Language: English







Introduction



Ill-posed problems



DSM for well-posed problems



DSM and linear ill-posed problems



Some inequalities



DSM for monotone operators



DSM for general nonlinear operator equations



DSM for operators satisfying a spectral assumption



DSM in Banach spaces



DSM and Newton-type methods without inversion of the derivative



DSM and unbounded operators



DSM and nonsmooth operators



DSM as a theoretical tool



DSM and iterative methods



Numerical problems arising in applications






Solving linear operator equations by a Newton-type DSM



DSM of gradient type for solving linear operator equations



DSM for solving linear equations with finite-rank operators



A discrepancy principle for equations with monotone continuous operators



DSM of Newton-type for solving operator equations with minimal smoothness assumptions



DSM of gradient type



DSM of simple iteration type



DSM for solving nonlinear operator equations in Banach spaces






Solving linear operator equations by the DSM



Stable solutions of Hammerstein-type integral equations



Inversion of the Laplace transform from the real axis using an adaptive iterative method