Title: Computing Small Singular Values of Bidiagonal Matrices With Guaranteed High Relative Accuracy Classic Reprint
Publisher: Forgotten Books
Publication Date: 2019
Language: English
ISBN 10: 1332870732
ISBN 13: 9781332870738
Binding: PAP
Condition: New
Weight: 136 grams

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Synopsis

This book is a groundbreaking analysis of the accuracy of singular value computations for bidiagonal matrices. Singular value decomposition is a fundamental tool in many scientific and engineering applications, but the accuracy of computed singular values has been a long-standing problem. The author presents a new algorithm for computing singular values that is guaranteed to produce high relative accuracy, even for small singular values. This is a significant advance over existing algorithms, which can suffer from large relative errors in computed singular values. The book also provides a detailed error analysis of the new algorithm, showing that it is stable and accurate even in the presence of rounding errors. This makes the algorithm suitable for use in a wide variety of applications. The book's insights into the accuracy of singular value computations are significant because they provide a foundation for understanding the behavior of singular value decomposition algorithms. This knowledge can be used to improve the accuracy of these algorithms and to develop new algorithms that are more efficient and reliable.

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