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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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- EditoreForgotten Books
- Data di pubblicazione2018
- ISBN 10 1334268533
- ISBN 13 9781334268533
- RilegaturaCopertina flessibile
- LinguaInglese
- Numero di pagine66
- Contatto del produttorenon disponibile
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Jacobi's Method Is More Accurate Than Qr Classic Reprint
Da: PBShop.store US, Wood Dale, IL, U.S.A.
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PAP. Condizione: New. New Book. Shipped from UK. Established seller since 2000. Codice articolo LX-9781334268533
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Jacobi's Method Is More Accurate Than Qr Classic Reprint
Da: PBShop.store UK, Fairford, GLOS, Regno Unito
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PAP. Condizione: New. New Book. Shipped from UK. Established seller since 2000. Codice articolo LX-9781334268533
Quantità: 15 disponibili
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Jacobi's Method Is More Accurate Than Qr (Classic Reprint)
Print on DemandDa: Forgotten Books, London, Regno Unito
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Paperback. Condizione: 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. Codice articolo 9781334268533_0
Quantità: Più di 20 disponibili