Dynamical systems method and applications : theoretical developments and numerical examples
 Author/Creator
 Ramm, A. G. (Alexander G.)
 Language
 English.
 Imprint
 Hoboken, N.J. : Wiley, c2012.
 Physical description
 xxix, 539 p. : ill. ; 25 cm.
Access
Available online

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QA614.8 .R35 2012

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QA614.8 .R35 2012
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Contributors
 Contributor
 Hoang, Nguyen S., 1980
Contents/Summary
 Bibliography
 Includes bibliographical references (p. 525535) and index.
 Contents

 PART I 1 Introduction 3 2 Illposed problems 11 3 DSM for wellposed problems 57 4 DSM and linear illposed 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 Newtontype 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 Newtontype DSM 255 17 DSM of gradient type for solving linear operator equations 269 18 DSM for solving linear equations with finiterank operators 281 19 A discrepancy principle for equations with monotone continuous operators 295 20 DSM of Newtontype 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 Hammersteintype integral equations 441 26 Inversion of the Laplace transform from the real axis using an adaptive iterative method 455.
 (source: Nielsen Book Data)
 Publisher's Summary
 Dynamical Systems Method (DSM) is a powerful general method for solving operator equations. These equations can be linear or nonlinear, wellposed or illposed. 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 illconditioned 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 illposed problems; wellposed problems; linear illposed problems; inequalities; monotone operators; general nonlinear operator equations; operators satisfying a spectral assumption; Banach spaces; Newtontype 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 illconditioned linear algebraic systems.
(source: Nielsen Book Data)
Subjects
Bibliographic information
 Publication date
 2012
 Responsibility
 Alexander G. Ramm, Nguyen S. Hoang.
 ISBN
 9781118024287 (cloth)
 1118024281 (cloth)