Iterative Methods For The Solution Of A Linear Operator Equation In Hilbert Space PDF Download
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Author | : W.M., III. Patterson |
Publisher | : Springer |
Total Pages | : 187 |
Release | : 2006-11-15 |
Genre | : Mathematics |
ISBN | : 3540384553 |
Download Iterative Methods for the Solution of a Linear Operator Equation in Hilbert Space Book in PDF, ePub and Kindle
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.
Author | : Walter Mead Patterson |
Publisher | : Lecture Notes in Mathematics |
Total Pages | : 202 |
Release | : 1974-07-22 |
Genre | : Mathematics |
ISBN | : |
Download Iterative Methods for the Solution of a Linear Operator Equation in Hilbert Space Book in PDF, ePub and Kindle
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.
Author | : W M III Patterson |
Publisher | : Springer |
Total Pages | : 196 |
Release | : 2014-01-15 |
Genre | : |
ISBN | : 9783662190166 |
Download Iterative Methods for the Solution of a Linear Operator Equation in Hilbert Space Book in PDF, ePub and Kindle
Author | : Michael Luther Hines |
Publisher | : |
Total Pages | : 168 |
Release | : 1976 |
Genre | : Hilbert space |
ISBN | : |
Download Iterative Methods for the Solution of Linear Operator Equations in Hilbert Space Book in PDF, ePub and Kindle
Author | : Walter Mead Patterson |
Publisher | : |
Total Pages | : |
Release | : 1974 |
Genre | : |
ISBN | : |
Download Iterative methods for the solution of linear operator equation in Hilbert space-A survey Book in PDF, ePub and Kindle
Author | : Gordon Wassermann |
Publisher | : |
Total Pages | : 282 |
Release | : 1974 |
Genre | : Categories (Mathematics) |
ISBN | : 9780387067940 |
Download Iterative Methods for the Solution of a Linear Operator Equation in Hilbert Space - a Survey Book in PDF, ePub and Kindle
Author | : Nikolaĭ Stepanovich Kurpelʹ |
Publisher | : American Mathematical Soc. |
Total Pages | : 204 |
Release | : 1976 |
Genre | : Mathematics |
ISBN | : 9780821815960 |
Download Projection-iterative Methods for Solution of Operator Equations Book in PDF, ePub and Kindle
Author | : M. Thamban Nair |
Publisher | : World Scientific |
Total Pages | : 264 |
Release | : 2009 |
Genre | : Mathematics |
ISBN | : 9812835652 |
Download Linear Operator Equations Book in PDF, ePub and Kindle
Many problems in science and engineering have their mathematical formulation as an operator equation Tx=y, where T is a linear or nonlinear operator between certain function spaces. In practice, such equations are solved approximately using numerical methods, as their exact solution may not often be possible or may not be worth looking for due to physical constraints. In such situations, it is desirable to know how the so-called approximate solution approximates the exact solution, and what the error involved in such procedures would be. This book is concerned with the investigation of the above theoretical issues related to approximately solving linear operator equations. The main tools used for this purpose are basic results from functional analysis and some rudimentary ideas from numerical analysis. To make this book more accessible to readers, no in-depth knowledge on these disciplines is assumed for reading this book.
Author | : Anatoly Galperin |
Publisher | : CRC Press |
Total Pages | : 241 |
Release | : 2016-11-17 |
Genre | : Mathematics |
ISBN | : 1498758967 |
Download Iterative Methods without Inversion Book in PDF, ePub and Kindle
Iterative Methods without Inversion presents the iterative methods for solving operator equations f(x) = 0 in Banach and/or Hilbert spaces. It covers methods that do not require inversions of f (or solving linearized subproblems). The typical representatives of the class of methods discussed are Ulm’s and Broyden’s methods. Convergence analyses of the methods considered are based on Kantorovich’s majorization principle which avoids unnecessary simplifying assumptions like differentiability of the operator or solvability of the equation. These analyses are carried out under a more general assumption about degree of continuity of the operator than traditional Lipschitz continuity: regular continuity. Key Features The methods discussed are analyzed under the assumption of regular continuity of divided difference operator, which is more general and more flexible than the traditional Lipschitz continuity. An attention is given to criterions for comparison of merits of various methods and to the related concept of optimality of a method of certain class. Many publications on methods for solving nonlinear operator equations discuss methods that involve inversion of linearization of the operator, which task is highly problematic in infinite dimensions. Accessible for anyone with minimal exposure to nonlinear functional analysis.
Author | : MOHAMMED ZUHAIR ZAKI NASHED |
Publisher | : |
Total Pages | : 340 |
Release | : 1963 |
Genre | : |
ISBN | : |
Download ITERATIVE METHODS FOR THE SOLUTIONS OF NONLINEAR OPERATOR EQUATIONS IN HILBERT SPACE. Book in PDF, ePub and Kindle