Computational Theory of Iterative Methods

Computational Theory of Iterative Methods
Title Computational Theory of Iterative Methods PDF eBook
Author Ioannis Argyros
Publisher Elsevier
Pages 505
Release 2007-09-04
Genre Mathematics
ISBN 0080560709

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The 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 mathematical programming and mathematical economics. There is also a huge number of exercises complementing the theory.- Latest convergence results for the iterative methods - Iterative methods with the least computational cost- Iterative methods with the weakest convergence conditions- Open problems on iterative methods

Aspects of the Computational Theory for Certain Iterative Methods

Aspects of the Computational Theory for Certain Iterative Methods
Title Aspects of the Computational Theory for Certain Iterative Methods PDF eBook
Author Ioannis K. Argyros
Publisher Polimetrica s.a.s.
Pages 581
Release 2009
Genre Mathematics
ISBN 8876991514

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Iterative Methods for Linear Systems

Iterative Methods for Linear Systems
Title Iterative Methods for Linear Systems PDF eBook
Author Maxim A. Olshanskii
Publisher SIAM
Pages 257
Release 2014-07-21
Genre Mathematics
ISBN 1611973465

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Iterative Methods for Linear Systems?offers a mathematically rigorous introduction to fundamental iterative methods for systems of linear algebraic equations. The book distinguishes itself from other texts on the topic by providing a straightforward yet comprehensive analysis of the Krylov subspace methods, approaching the development and analysis of algorithms from various algorithmic and mathematical perspectives, and going beyond the standard description of iterative methods by connecting them in a natural way to the idea of preconditioning.??

The Theory and Applications of Iteration Methods

The Theory and Applications of Iteration Methods
Title The Theory and Applications of Iteration Methods PDF eBook
Author Ioannis K. Argyros
Publisher CRC Press
Pages 471
Release 2022-01-20
Genre Mathematics
ISBN 1000536750

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The theory and applications of Iteration Methods is a very fast-developing field of numerical analysis and computer methods. The second edition is completely updated and continues to present the state-of-the-art contemporary theory of iteration methods with practical applications, exercises, case studies, and examples of where and how they can be used. The Theory and Applications of Iteration Methods, Second Edition includes newly developed iteration methods taking advantage of the most recent technology (computers, robots, machines). It extends the applicability of well-established methods by increasing the convergence domain and offers sharper error tolerance. New proofs and ideas for handling convergence are introduced along with a new variety of story problems picked from diverse disciplines. This new edition is for researchers, practitioners, and students in engineering, economics, and computational sciences.

Iterative Methods for Sparse Linear Systems

Iterative Methods for Sparse Linear Systems
Title Iterative Methods for Sparse Linear Systems PDF eBook
Author Yousef Saad
Publisher SIAM
Pages 537
Release 2003-04-01
Genre Mathematics
ISBN 0898715342

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Mathematics of Computing -- General.

A Contemporary Study of Iterative Methods

A Contemporary Study of Iterative Methods
Title A Contemporary Study of Iterative Methods PDF eBook
Author A. Alberto Magrenan
Publisher Academic Press
Pages 402
Release 2018-02-13
Genre Mathematics
ISBN 0128094931

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A Contemporary Study of Iterative Methods: Convergence, Dynamics and Applications evaluates and compares advances in iterative techniques, also discussing their numerous applications in applied mathematics, engineering, mathematical economics, mathematical biology and other applied sciences. It uses the popular iteration technique in generating the approximate solutions of complex nonlinear equations that is suitable for aiding in the solution of advanced problems in engineering, mathematical economics, mathematical biology and other applied sciences. Iteration methods are also applied for solving optimization problems. In such cases, the iteration sequences converge to an optimal solution of the problem at hand. - Contains recent results on the convergence analysis of numerical algorithms in both finite-dimensional and infinite-dimensional spaces - Encompasses the novel tool of dynamic analysis for iterative methods, including new developments in Smale stability theory and polynomiography - Explores the uses of computation of iterative methods across non-linear analysis - Uniquely places discussion of derivative-free methods in context of other discoveries, aiding comparison and contrast between options

Computational Methods for Inverse Problems

Computational Methods for Inverse Problems
Title Computational Methods for Inverse Problems PDF eBook
Author Curtis R. Vogel
Publisher SIAM
Pages 195
Release 2002-01-01
Genre Mathematics
ISBN 0898717574

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Provides a basic understanding of both the underlying mathematics and the computational methods used to solve inverse problems.