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Excerpt from Optimal Preconditioners of a Given Sparsity Pattern
To make this bound small, it should be close to 1. This bound is sharp for the Chebyshev method, in the sense that there is an initial guess for which the bound will be attained at every step. It is not sharp for the conjugate gradient method. A sharp error bound for the conjugate gradient method is more complicated involving the distribution of all eigen values of m'la, but a condition number1 x(ma) close to 1 is sufficient to ensure fast con vergence of this algorithm as well, even when the effects of finite precision arithmetic are taken into account Therefore, we will define optimality in terms of the condition number k(m-1a) and minimization of this quantity will be our goal.
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- PublisherForgotten Books
- Publication date2020
- ISBN 10 1332173497
- ISBN 13 9781332173495
- BindingPaperback
- LanguageEnglish
- Number of pages41
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Optimal Preconditioners of a Given Sparsity Pattern (Classic Reprint)
Print on DemandSeller: Forgotten Books, London, United Kingdom
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Paperback. Condition: New. Print on Demand. This book, shedding insightful light on the practicalities of improving matrix computation, focuses on the difficulties of finding efficient preconditioners and presents a useful tool for their study. Particularly relevant to those working with elliptic partial differential equations, the author provides a practical means of gaining a deeper understanding of preconditioners and their effectiveness for a given matrix. Explaining the use of optimization techniques to efficiently tackle the problem of minimizing a particular convex function, the author goes on to present and discuss a variety of insightful experiments concluding that the preconditioner returned by the optimization code can be significantly better than many currently used preconditioners, giving the reader an invaluable head start in pushing their research further. 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 # 9781332173495_0
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Optimal Preconditioners of a Given Sparsity Pattern Classic Reprint
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PAP. Condition: New. New Book. Shipped from UK. Established seller since 2000. Seller Inventory # LW-9781332173495
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Optimal Preconditioners of a Given Sparsity Pattern Classic Reprint
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PAP. Condition: New. New Book. Shipped from UK. Established seller since 2000. Seller Inventory # LW-9781332173495
Quantity: 15 available