Jacobi's Method Is More Accurate Than Qr Classic Reprint

James Demmel

ISBN 10: 1334268533 ISBN 13: 9781334268533

Published by Forgotten Books, 2018

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Excerpt from Jacobi's Method Is More Accurate Than Qr

These results depend on new perturbation theorems for eigenvalues and eigenvectors (or singular values and singular vectors) as well as a new error analysis of Jacobi, all of which are stronger than their classical counterparts. They also depend on an empirical observa tion for which we have overwhelming numerical evidence but somewhat weaker theoretical understanding.

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Title: Jacobi's Method Is More Accurate Than Qr ...
Publisher: Forgotten Books
Publication Date: 2018
Binding: PAP
Condition: New

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Jacobi's Method Is More Accurate Than Qr (Classic Reprint)

James Demmel, Kresimir Veselic

Published by Forgotten Books, 2018

ISBN 10: 1334268533 ISBN 13: 9781334268533

New Paperback

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Seller: Forgotten Books, London, United Kingdom

Seller rating 5 out of 5 stars

Paperback. Condition: New. Print on Demand. This book explores the effectiveness of Jacobi and QR methods in calculating eigenvalues and singular values. The author demonstrates that Jacobi methods yield higher accuracy than QR, and can attain optimal accuracy when componentwise relative uncertainties in the matrix entries are small. The book begins by introducing perturbation theory for eigenvalues and singular values, providing new insights into the sensitivity of these quantities to matrix perturbations. It then analyzes two-sided Jacobi for the symmetric positive definite eigenproblem, proving that it computes eigenvalues with near-optimal accuracy. The author also discusses one-sided Jacobi for the singular value decomposition, showing that it achieves similar accuracy. The book's significance lies in its rigorous mathematical analysis of Jacobi methods, providing a theoretical foundation for their effectiveness in practical computations. By clarifying the conditions under which Jacobi methods attain high accuracy, this book empowers researchers and practitioners to make informed choices when solving eigenvalue and singular value problems. 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 # 9781334268533_0

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