Published by Hardpress Publishing, 2013
ISBN 10: 131495136X ISBN 13: 9781314951363
Language: English
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Published by Hardpress Publishing, 2013
ISBN 10: 131495136X ISBN 13: 9781314951363
Language: English
Seller: PBShop.store UK, Fairford, GLOS, United Kingdom
PAP. Condition: New. New Book. Shipped from UK. Established seller since 2000.
Seller: PBShop.store US, Wood Dale, IL, U.S.A.
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Published by Franklin Classics 10/15/2018, 2018
ISBN 10: 0343206897 ISBN 13: 9780343206895
Language: English
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Paperback. Condition: new. Paperback. This study analyzes the accuracy of Jacobi's method in comparison to the QR algorithm for matrix computations. Originally published in 1988, "Jacobi's Method is More Accurate Than QR" presents a rigorous mathematical treatment demonstrating the circumstances under which Jacobi's method offers superior precision. The research contributes valuable insights to the field of numerical analysis and is useful to researchers and practitioners dealing with eigenvalue problems and matrix diagonalization.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. Shipping may be from our UK warehouse or from our Australian or US warehouses, depending on stock availability.
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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.
Hardcover. Condition: new. Hardcover. This study analyzes the accuracy of Jacobi's method in comparison to the QR algorithm for matrix computations. Originally published in 1988, "Jacobi's Method is More Accurate Than QR" presents a rigorous mathematical treatment demonstrating the circumstances under which Jacobi's method offers superior precision. The research contributes valuable insights to the field of numerical analysis and is useful to researchers and practitioners dealing with eigenvalue problems and matrix diagonalization.This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work.This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant. Shipping may be from our UK warehouse or from our Australian or US warehouses, depending on stock availability.