Iterative Methods For The Solution Of Linear Operator Equations In Hilbert Space
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Iterative Methods For The Solution Of A Linear Operator Equation In Hilbert Space
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Author : W.M., III. Patterson
language : en
Publisher: Springer
Release Date : 2006-11-15
Iterative Methods For The Solution Of A Linear Operator Equation In Hilbert Space written by W.M., III. Patterson and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
In this expository work we shall conduct a survey of iterative techniques for solving the linear operator equations Ax=y in a Hilbert space. Whenever convenient these iterative schemes are given in the context of a complex Hilbert space -- Chapter II is devoted to those methods (three in all) which are given only for real Hilbert space. Thus chapter III covers those methods which are valid in a complex Hilbert space except for the two methods which are singled out for special attention in the last two chapters. Specifically, the method of successive approximations is covered in Chapter IV, and Chapter V consists of a discussion of gradient methods. While examining these techniques, our primary concern will be with the convergence of the sequence of approximate solutions. However, we shall often look at estimates of the error and the speed of convergence of a method.
Iterative Methods For The Solution Of A Linear Operator Equation In Hilbert Space A Survey
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Author : Walter Mead Patterson
language : en
Publisher:
Release Date : 1974
Iterative Methods For The Solution Of A Linear Operator Equation In Hilbert Space A Survey written by Walter Mead Patterson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with Hilbert space categories.
Iterative Methods For The Solution Of A Linear Operator Equation In Hilbert Space
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Author : W M III Patterson
language : en
Publisher: Springer
Release Date : 2014-01-15
Iterative Methods For The Solution Of A Linear Operator Equation In Hilbert Space written by W M III Patterson and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Iterative Methods For The Solution Of Linear Operator Equations In Hilbert Space
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Author : Michael Luther Hines
language : en
Publisher:
Release Date : 1976
Iterative Methods For The Solution Of Linear Operator Equations In Hilbert Space written by Michael Luther Hines and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976 with Hilbert space categories.
Iterative Methods For The Solution Of Linear Operator Equation In Hilbert Space A Survey
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Author : Walter Mead Patterson
language : de
Publisher:
Release Date : 1974
Iterative Methods For The Solution Of Linear Operator Equation In Hilbert Space A Survey written by Walter Mead Patterson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with categories.
Hilbert Space Splittings And Iterative Methods
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Author : Michael Griebel
language : en
Publisher: Springer Nature
Release Date : 2024-11-06
Hilbert Space Splittings And Iterative Methods written by Michael Griebel and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-11-06 with Mathematics categories.
This book is about the theory of so-called Schwarz methods for solving variational problems in a Hilbert space V arising from linear equations and their associated quadratic minimization problems. Schwarz methods are based on the construction of a sequence of approximate solutions by solving auxiliary variational problems on a set of (smaller, finite-dimensional) Hilbert spaces $V_i$ in a certain order, combining them, and using the combined approximations in an iterative procedure. The spaces $V_i$ form a so-called space splitting for V, they need not necessarily be subspaces of V, and their number can be finite or infinite. The convergence behavior of Schwarz methods is influenced by certain properties of the space splittings they are based on. These properties are identified, and a detailed treatment of traditional deterministic and more recent greedy and stochastic orderings in the subproblem solution process is given, together with an investigation of accelerated methods. To illustrate the abstract theory, the numerical linear algebra analogs of the iterative methods covered in the book are discussed. Its standard application to the convergence theory of multilevel and domain decomposition methods for solving PDE problems is explained, and links to optimization theory and online learning algorithms are given. Providing an introduction and overview of iterative methods which are based on problem decompositions and suitable for parallel and distributed computing, the book could serve as the basis for a one- or two-semester course for M.S. and Ph.D. students specializing in numerical analysis and scientific computing. It will also appeal to a wide range of researchers interested in scientific computing in the broadest sense.
Iterative Methods For Approximate Solution Of Inverse Problems
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Author : A.B. Bakushinsky
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-09-28
Iterative Methods For Approximate Solution Of Inverse Problems written by A.B. Bakushinsky and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-09-28 with Mathematics categories.
This volume presents a unified approach to constructing iterative methods for solving irregular operator equations and provides rigorous theoretical analysis for several classes of these methods. The analysis of methods includes convergence theorems as well as necessary and sufficient conditions for their convergence at a given rate. The principal groups of methods studied in the book are iterative processes based on the technique of universal linear approximations, stable gradient-type processes, and methods of stable continuous approximations. Compared to existing monographs and textbooks on ill-posed problems, the main distinguishing feature of the presented approach is that it doesn’t require any structural conditions on equations under consideration, except for standard smoothness conditions. This allows to obtain in a uniform style stable iterative methods applicable to wide classes of nonlinear inverse problems. Practical efficiency of suggested algorithms is illustrated in application to inverse problems of potential theory and acoustic scattering. The volume can be read by anyone with a basic knowledge of functional analysis. The book will be of interest to applied mathematicians and specialists in mathematical modeling and inverse problems.
Iterative Methods For The Solutions Of Non Linear Operator Equations In Hilbert Space
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Author : M. Zuhair Nashed
language : en
Publisher:
Release Date : 1963
Iterative Methods For The Solutions Of Non Linear Operator Equations In Hilbert Space written by M. Zuhair Nashed and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1963 with Equations categories.
The Numerical Solution Of Integral Equations Of The Second Kind
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Author : Kendall E. Atkinson
language : en
Publisher: Cambridge University Press
Release Date : 1997-06-28
The Numerical Solution Of Integral Equations Of The Second Kind written by Kendall E. Atkinson and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-06-28 with Mathematics categories.
This book provides an extensive introduction to the numerical solution of a large class of integral equations.
Integral Equations And Iteration Methods In Electromagnetic Scattering
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Author : A. B. Samokhin
language : en
Publisher: Walter de Gruyter
Release Date : 2013-03-12
Integral Equations And Iteration Methods In Electromagnetic Scattering written by A. B. Samokhin and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-12 with Mathematics categories.
No detailed description available for "Integral Equations and Iteration Methods in Electromagnetic Scattering".