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Excerpt from Gmres/Cr and Arnoldi/Lanczos as Matrix Approximation Problems
A comparison of (1) and (2) suggests that from an approximation point of view, the difference between the gmres and Arnoldi algorithms is slight. This analogy is rarely brought out in accounts of these algorithms, partly for historical reasons and partly because the usual applications of the two algorithms are differ ent. Whereas gmres is applied to solve systems of equations A3: b, so that (1) comes quickly to mind as a description of it, the Arnoldi iteration is traditionally thought of as a method for estimating eigenvalues of A. The Arnoldi eigenvalue estimatesl at step n are the eigenvalues of H, that is, the roots of p. But what the Arnoldi iteration actually does is solve its connection with eigenvalues is indirect and approximate.
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- PublisherForgotten Books
- Publication date2024
- ISBN 10 133369038X
- ISBN 13 9781333690380
- BindingPaperback
- LanguageEnglish
- Number of pages25
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Gmres/Cr and Arnoldi/Lanczos as Matrix Approximation Problems (Classic Reprint)
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Paperback. Condition: New. Print on Demand. This book examines the Arnoldi and GMRES algorithms, two numerical methods for solving matrix equations, within the framework of approximation theory. The author demonstrates that these algorithms seek to approximate certain matrix problems. The author discusses why this finding is important and the advantages of understanding these matrix equations within the context of approximation theory. 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 # 9781333690380_0
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GmresCr and ArnoldiLanczos as Matrix Approximation Problems Classic Reprint
Seller: PBShop.store US, Wood Dale, IL, U.S.A.
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PAP. Condition: New. New Book. Shipped from UK. Established seller since 2000. Seller Inventory # LX-9781333690380
Quantity: 15 available
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GmresCr and ArnoldiLanczos as Matrix Approximation Problems 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 # LX-9781333690380
Quantity: 15 available