Iterative Methods For The Solution Of A Linear Operator Equation 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 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.

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 Sparse Linear Systems

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Author : Yousef Saad
language : en
Publisher: SIAM
Release Date : 2003-04-01

Iterative Methods For Sparse Linear Systems written by Yousef Saad and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-04-01 with Mathematics categories.

Mathematics of Computing -- General.

New Splitting Iterative Methods For Solving Multidimensional Neutron Transport Equations

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Author : Jacques Tagoudjeu
language : en
Publisher: Universal-Publishers
Release Date : 2011-04

New Splitting Iterative Methods For Solving Multidimensional Neutron Transport Equations written by Jacques Tagoudjeu and has been published by Universal-Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-04 with Mathematics categories.

This thesis focuses on iterative methods for the treatment of the steady state neutron transport equation in slab geometry, bounded convex domain of Rn (n = 2,3) and in 1-D spherical geometry. We introduce a generic Alternate Direction Implicit (ADI)-like iterative method based on positive definite and m-accretive splitting (PAS) for linear operator equations with operators admitting such splitting. This method converges unconditionally and its SOR acceleration yields convergence results similar to those obtained in presence of finite dimensional systems with matrices possessing the Young property A. The proposed methods are illustrated by a numerical example in which an integro-differential problem of transport theory is considered. In the particular case where the positive definite part of the linear equation operator is self-adjoint, an upper bound for the contraction factor of the iterative method, which depends solely on the spectrum of the self-adjoint part is derived. As such, this method has been successfully applied to the neutron transport equation in slab and 2-D cartesian geometry and in 1-D spherical geometry. The self-adjoint and m-accretive splitting leads to a fixed point problem where the operator is a 2 by 2 matrix of operators. An infinite dimensional adaptation of minimal residual and preconditioned minimal residual algorithms using Gauss-Seidel, symmetric Gauss-Seidel and polynomial preconditioning are then applied to solve the matrix operator equation. Theoretical analysis shows that the methods converge unconditionally and upper bounds of the rate of residual decreasing which depend solely on the spectrum of the self-adjoint part of the operator are derived. The convergence of theses solvers is illustrated numerically on a sample neutron transport problem in 2-D geometry. Various test cases, including pure scattering and optically thick domains are considered.

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 A Linear Operator Equation In Hilbert Space A Survey

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Author : Gordon Wassermann
language : en
Publisher:
Release Date : 1974

Iterative Methods For The Solution Of A Linear Operator Equation In Hilbert Space A Survey written by Gordon Wassermann 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 (Mathematics) 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.