Computing Accurate Eigensystems of Scaled Diagonally Dominant Matrices
Language: English
Published by Forgotten Books, 2018
- Softcover
- New
Seller: Forgotten Books, London, United KingdomForgotten Books
AbeBooks seller since June 2, 2021
Condition: New
£ 13.45
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Add to basketItem description from seller
Print on Demand. This book examines the computation of scaled diagonally dominant matrices, a type of matrix often arising from mathematical models. The author provides a mathematical framework to analyze the accuracy of computations on these matrices, proving error bounds for eigenvalues, singular values, and eigenvectors. The book extends existing results for bidiagonal and tridiagonal matrices to eigenvalues and singular values of much more general matrices. The ideas are presented in a unified way, providing a new theoretical foundation for understanding the numerical behavior of diagonally dominant matrices, and offers improved algorithms for the accurate computation of eigenvalues, singular values, and eigenvectors. The theoretical framework will be of interest to researchers and practitioners in numerical analysis, while the improved algorithms may prove valuable to scientists and engineers using these matrices in their work. 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.…
Seller Inventory # 9781332115419_0
- Title
- Computing Accurate Eigensystems of Scaled Diagonally Dominant Matrices
- Author
- J. Barlow, J. Demmel
- Publisher
- Forgotten Books
- Publication year
- 2018
- Condition
- New
- Book Type
- print-on-demand item
- Binding
- Paperback
- Language
- English
- ISBN 10
- 1332115411
- ISBN 13
- 9781332115419
- Seller catalogs
- Calculus
A rigorous exploration of how small changes in matrix entries affect eigenvalues and singular values. The work develops a unified perturbation theory for symmetric scaled diagonally dominant matrices and s.d.d. pencils, with a focus on high relative accuracy.
Two short paragraphs framing scope and value:
This edition extends prior results from bidiagonal matrices to broader classes, including symmetric s.d.d. matrices and definite pencils. It presents stability theorems, new bounds, and practical algorithms that achieve high relative accuracy for both eigenvalues and eigenvectors, even when magnitudes vary greatly. The text also connects theory to algorithms such as bisection, specialized QR variants, and inverse iteration, with attention to numerical reliability in finite precision.
- Learn how scaled diagonal dominance improves perturbation bounds and accuracy.
- Understand the relative gap concept and how it strengthens eigenvector sensitivity results.
- See how stable algorithms compute eigenvalues, eigenvectors, and inertia with high relative precision.
- Explore applications to differential operators and broader implications for numerical linear algebra.
Closing line: Ideal for readers working in numerical analysis, applied mathematics, and engineering who need reliable eigenvalue computations in challenging matrix classes.
"Synopsis" may belong to another edition of this title.
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Forgotten Books’ Classic Reprint Series utilizes the latest technology to regenerate facsimiles of historically important writings. Careful attention has been made to accurately preserve the original format of each page whilst digitally enhancing the quality of the aged text.
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Forgotten Books publishes hundreds of thousands of rare and classic books.
This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
This text has been digitally restored from a historical edition. Some errors may persist, however we consider it worth publishing due to the work's historical value.
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