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Dynamical Systems Method and Applications Theoretical Developments and Numerical Examples

ISBN-10: 1118024281

ISBN-13: 9781118024287

Edition: 2012

Authors: Alexander G. Ramm, Nguyen S. Hoang

List price: $222.95
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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 problems; well-posed problems; linear ill-posed problems; inequalities; monotone operators; general nonlinear operator equations; operators satisfying a spectral assumption; Banach spaces; Newton-type methods without inversion of the derivative; unbound operators; nonsmooth operators; DSM as a theoretical tool; iterative methods; numerical problems arising in applications; auxiliary results from analysis; a discrepancy principle for solving equations with monotone operators; solving linear equations; stable numerical differentiation; deconvolution problems; numerical implementation; and stable solution to ill-conditioned linear algebraic systems.
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Book details

List price: $222.95
Copyright year: 2012
Publisher: John Wiley & Sons, Incorporated
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