Download or read book Iterative Methods for the Solution of a Linear Operator Equation in Hilbert Space written by W.M., III. Patterson and published by Springer. This book was released on 2006-11-15 with total page 187 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Iterative Methods for the Solution of a Linear Operator Equation in Hilbert Space a Survey written by Walter Mead Patterson and published by . This book was released on 1974 with total page 183 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Iterative Methods for the Solution of a Linear Operator Equation in Hilbert Space written by W M III Patterson and published by Springer. This book was released on 2014-01-15 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Iterative methods for the solution of linear operator equation in Hilbert space A survey written by Walter Mead Patterson and published by . This book was released on 1974 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Iterative Methods for the Solution of a Linear Operator Equation in Hilbert Space a Survey written by Gordon Wassermann and published by . This book was released on 1974 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Iterative Methods for the Solution of Linear Operator Equations in Hilbert Space written by Michael Luther Hines and published by . This book was released on 1976 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Projection iterative Methods for Solution of Operator Equations written by Nikolaĭ Stepanovich Kurpelʹ and published by American Mathematical Soc.. This book was released on 1976 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Iterative Methods without Inversion written by Anatoly Galperin and published by CRC Press. This book was released on 2016-11-17 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Iterative Methods for Ill Posed Problems written by Anatoly B. Bakushinsky and published by Walter de Gruyter. This book was released on 2010-12-23 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ill-posed problems are encountered in countless areas of real world science and technology. A variety of processes in science and engineering is commonly modeled by algebraic, differential, integral and other equations. In a more difficult case, it can be systems of equations combined with the associated initial and boundary conditions. Frequently, the study of applied optimization problems is also reduced to solving the corresponding equations. These equations, encountered both in theoretical and applied areas, may naturally be classified as operator equations. The current textbook will focus on iterative methods for operator equations in Hilbert spaces.

Download or read book Interative Methods for the Solution of a Linear Operator Equation in Hilbert Space a Survey written by W.M. Patterson (III.) and published by . This book was released on 1974 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book ITERATIVE METHODS FOR THE SOLUTIONS OF NONLINEAR OPERATOR EQUATIONS IN HILBERT SPACE written by MOHAMMED ZUHAIR ZAKI NASHED and published by . This book was released on 1963 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Iterative Methods for Sparse Linear Systems written by Yousef Saad and published by SIAM. This book was released on 2003-04-01 with total page 537 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematics of Computing -- General.

Download or read book Direct and Iterative Methods for the Solution of Linear Operator Equations in Hilbert Space written by Wolodymyr V. Petryshyn and published by . This book was released on 1961 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Iterative Methods for Nonlinear Ill Posed Problems written by Atef Ibrahim Elmahdy and published by LAP Lambert Academic Publishing. This book was released on 2012-04 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many problems in science and engineering have their mathematical formulation as an operator equation of the form F(x) = y, where F 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 be often possible or may not be worth looking for due to physical constraints. In such situation, it is desirable to know how the so-called approximate solution approximates the exact solution, and what would be the error involved in such procedures. The main focus of the book is on the study of stably solving nonlinear ill posed operator equations of the form F(x)=y, with monotone nonlinear operator F in an infinite dimensional real Hilbert space X, that is , F obeys the monotonicity property. It is assumed that the exact data y is unknown and usually only noisy data are available. Problems of this type arise in a number of applications. Since the solution does not depend continuously on the data, the ill-posed problem has to be regularized. We considered iterative methods which converge to the unique solution of the method of Lavrentiev regularization.

Download or read book A Survey of Preconditioned Iterative Methods written by Are Magnus Bruaset and published by Routledge. This book was released on 2018-12-13 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: The problem of solving large, sparse, linear systems of algebraic equations is vital in scientific computing, even for applications originating from quite different fields. A Survey of Preconditioned Iterative Methods presents an up to date overview of iterative methods for numerical solution of such systems. Typically, the methods considered are w

Download or read book Convergence of Iterations for Linear Equations written by Olavi Nevanlinna and published by Birkhäuser. This book was released on 2012-12-06 with total page 187 pages. Available in PDF, EPUB and Kindle. Book excerpt: Assume that after preconditioning we are given a fixed point problem x = Lx + f (*) where L is a bounded linear operator which is not assumed to be symmetric and f is a given vector. The book discusses the convergence of Krylov subspace methods for solving fixed point problems (*), and focuses on the dynamical aspects of the iteration processes. For example, there are many similarities between the evolution of a Krylov subspace process and that of linear operator semigroups, in particular in the beginning of the iteration. A lifespan of an iteration might typically start with a fast but slowing phase. Such a behavior is sublinear in nature, and is essentially independent of whether the problem is singular or not. Then, for nonsingular problems, the iteration might run with a linear speed before a possible superlinear phase. All these phases are based on different mathematical mechanisms which the book outlines. The goal is to know how to precondition effectively, both in the case of "numerical linear algebra" (where one usually thinks of first fixing a finite dimensional problem to be solved) and in function spaces where the "preconditioning" corresponds to software which approximately solves the original problem.

Download or read book Iterative Solution of Symmetric Quasi Definite Linear Systems written by Dominique Orban and published by SIAM. This book was released on 2017-04-07 with total page 101 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerous applications, including computational optimization and fluid dynamics, give rise to block linear systems of equations said to have the quasi-definite structure. In practical situations, the size or density of those systems can preclude a factorization approach, leaving only iterative methods as the solution technique. Known iterative methods, however, are not specifically designed to take advantage of the quasi-definite structure. This book discusses the connection between quasi-definite systems and linear least-squares problems, the most common and best understood problems in applied mathematics, and explains how quasi-definite systems can be solved using tailored iterative methods for linear least squares (with half as much work!). To encourage researchers and students to use the software, it is provided in MATLAB, Python, and Julia. The authors provide a concise account of the most well-known methods for symmetric systems and least-squares problems, research-level advances in the solution of problems with specific illustrations in optimization and fluid dynamics, and a website that hosts software in three languages.