Convergence of a Two-Stage Richardson Iterative Procedure for Solving Systems

Gene H. Golub, Michael L. Overton

ISBN 10: 1333246897 / ISBN 13: 9781333246891

Editore: Forgotten Books, 2024

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Print on Demand. This book delineates a novel approach to solving systems of linear equations, widely used in scientific computations. The author introduces a technique known as the Richardson method, a second-order scheme that approximates solutions iteratively. The text offers a detailed exposition of the method's convergence properties, providing a theoretical foundation for its practical application. Additionally, the author explores extensions of the method to handle more complex linear systems, including those with symmetric and skew-symmetric components. Through numerical experiments and mathematical analysis, the book demonstrates the effectiveness of the Richardson method in solving real-world problems, offering valuable insights for researchers and practitioners in scientific computing, engineering, and other fields that rely heavily on solving systems of equations. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. Codice articolo 9781333246891_0

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Titolo: Convergence of a Two-Stage Richardson ...

Casa editrice: Forgotten Books

Data di pubblicazione: 2024

Legatura: Paperback

Condizione: New

Tipologia articolo: print-on-demand item

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Excerpt from Convergence of a Two-Stage Richardson Iterative Procedure for Solving Systems of Linear Equations

One motivation for our work is that the two-stage method can be effectively used to solve nonsymmetric systems where M is symmetric positive definite and N is~skewfsymmetric. In this case the symmetric/ skew-symmetric splitting A -n:is used to precondition the outer itera tion, and a symmetric splitting-m ml-m2 can be used to precondition each inner iteration, using a direct method to solve a system of the form Mly c at each step of-each inner iteration. (see Manteuffel (1977) for alternative approaches for nonsymmetric systems.) Numerical results from applying the Richardson method to such nonsymmetric systems are given in Section 3. We also present-numerical results using the conjugate gradient method for the outer iteration. Analysis of the latter procedure would be very interesting, but this seems more diffi cult.

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This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.