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Iterative Krylov Methods for Large Linear Systemsby Henk A. van der Vorst; P. G. Ciarlet; A. Iserles; R. V. Kohn; M. H. Wright
Cambridge University Press 2003; US$ 38.00Based on extensive teaching by the author, this book presents an overview of a number of Krylov projection methods for the solution of linear systems of equations. There are a large number of references for further reading as well as exercises to help students as they first encounter the material. more...
Computational Theory of Iterative Methodsby Ioannis Argyros
Elsevier 2007; US$ 215.00The book is designed for researchers, students and practitioners interested in using fast and efficient iterative methods to approximate solutions of nonlinear equations. The following four major problems are addressed. Problem 1: Show that the iterates are well defined. Problem 2: concerns the convergence of the sequences generated by a process and the question of whether the limit points are, in fact solutions of the equation. Problem 3: concerns the economy of the entire operations. Problem 4: concerns with how to best choose a method, algorithm or software program to solve a specific type of problem and its description of when a given algorithm succeeds or fails. The book contains applications in several areas of applied sciences including... more...
Convergence and Applications of Newton-type Iterationsby Ioannis K. Argyros
Springer 2008; US$ 79.95Recent results in local convergence and semi-local convergence analysis constitute a natural framework for the theoretical study of iterative methods. This monograph provides a comprehensive study of both basic theory and new results in the area. Each chapter contains new theoretical results and important applications in engineering, dynamic economic systems, input-output systems, optimization problems, and nonlinear and linear differential equations. Several classes of operators are considered, including operators without Lipschitz continuous derivatives, operators with high order derivatives, and analytic operators. Each section is self-contained. Examples are used to illustrate the theory and exercises are included at the end of each chapter.... more...
Operators and Iterative Processes of Fejér Typeby Vladimir V Vasin; Ivan I. Eremin
Walter de Gruyter, Inc. 2009; US$ 140.00This book, written by two experts in the field, deals with classes of iterative methods for the approximate solution of fixed points equations for operators satisfying a special contractivity condition, the Fejér property. The book is elementary, self-contained and uses methods from functional analysis, with a special focus on the construction of iterative schemes. Applications to parallelization, randomization and linear programming are also considered. more...
Some successive approximation methods in control and oscillation theoryby Peter L. Falb; Jan L de Jong
Elsevier Science & Technology 1969; US$ 161.00In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation; methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; and methods for information compression... more...
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