Relaxation Methods for Linear Equations (Classic Reprint) - Hardcover

Samuel Schechter

9780484598736: Relaxation Methods for Linear Equations (Classic Reprint)

Hardcover

ISBN 10: 0484598732 ISBN 13: 9780484598736

Publisher: Forgotten Books, 2018

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Efficient ways to solve linear systems with relaxation methods

This book presents how to solve Au = b by simple iterative steps that adjust one or a few components at a time. It explains the historical roots of relaxation and how different update choices affect convergence, including when and why a method converges for certain matrix types.

Structured for practitioners, it covers both scalar and group (block) updates. You’ll see how choosing the most troublesome equation at each step can speed up convergence, and how residuals guide the process. The text also introduces a framework for analyzing convergence with positive definite matrices and extends results to more complex, automatically coded schemes.

How relaxation fits into solving discretized boundary-value problems
Conditions that guarantee convergence for complete or approximate (over/under) relaxation
The idea of grouping variables and applying small matrix inverses to speed up iterations
Strategies for ordering updates and comparing cyclic versus residually ordered methods

Ideal for readers who want a clear, math‑grounded path from the basic idea to practical algorithms, with proofs and examples that illuminate when these methods work best. This edition is suited to students and professionals seeking a solid foundation in relaxation techniques for linear equations.

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