Synopsis
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
"synopsis" may belong to another edition of this title.
Other Popular Editions of the Same Title
Search results for Relaxation Methods for Linear Equations (Classic Reprint)
Stock Image
Relaxation Methods for Linear Equations (Classic Reprint)
Print on DemandSeller: Forgotten Books, London, United Kingdom
Seller rating 4 out of 5 stars
Paperback. Condition: New. 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. print-on-demand item. Seller Inventory # 9781333036539_0
Buy New
US$ 17.58
Free Shipping
Ships from United Kingdom to U.S.A.
Ships from United Kingdom to U.S.A.
Quantity: Over 20 available
Stock Image
Relaxation Methods for Linear Equations Classic Reprint
Seller: PBShop.store US, Wood Dale, IL, U.S.A.
Seller rating 5 out of 5 stars
PAP. Condition: New. New Book. Shipped from UK. Established seller since 2000. Seller Inventory # LW-9781333036539
Stock Image
Relaxation Methods for Linear Equations Classic Reprint
Seller: PBShop.store UK, Fairford, GLOS, United Kingdom
Seller rating 5 out of 5 stars
PAP. Condition: New. New Book. Shipped from UK. Established seller since 2000. Seller Inventory # LW-9781333036539
Buy New
US$ 28.11
US$ 4.38 shipping
Ships from United Kingdom to U.S.A.
Ships from United Kingdom to U.S.A.
Quantity: 15 available