Relaxation Methods for Linear Equations (Classic Reprint)
Language: English
Published by Forgotten Books, 2018
- Softcover
- New
Seller: Forgotten Books, London, United KingdomForgotten Books
AbeBooks seller since June 2, 2021
Condition: New
US$ 17.58
Quantity: Over 20 available
Add to basketItem description from seller
Print on Demand. This book explores a numerical technique known as relaxation methods, which were originally introduced by Gauss to solve systems of linear equations. The author extends these methods to group relaxation techniques and presents new insights into approximate relaxation. Complete convergence and free steering theorems are proven for positive definite symmetric matrices, extending the work of Temple and Ostrowski. The author also provides explicit error estimates and considers special cases such as matrices with non-negative inverses. These methods have been successfully applied by Southwell and others to boundary value problems and are particularly well-suited for use on automatic digital computers. 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.
Seller Inventory # 9781333036539_0
- Title
- Relaxation Methods for Linear Equations (Classic Reprint)
- Author
- Samuel Schechter
- Publisher
- Forgotten Books
- Publication year
- 2018
- Condition
- New
- Book Type
- print-on-demand item
- Binding
- Paperback
- Language
- English
- ISBN 10
- 1333036531
- ISBN 13
- 9781333036539
- Seller catalogs
- Calculus
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
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Forgotten Books
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Forgotten Books’ Classic Reprint Series utilizes the latest technology to regenerate facsimiles of historically important writings. Careful attention has been made to accurately preserve the original format of each page whilst digitally enhancing the quality of the aged text.
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