T�tulo: Computing Small Singular Values of Bidiagonal Matrices With Guaranteed High Relative Accuracy Classic Reprint
Editor: Forgotten Books
Fecha de publicaci�n: 2019
Idioma: Ingl�s
ISBN 10: 1332870732
ISBN 13: 9781332870738
Encuadernaci�n: PAP
Estado: New
Peso: 136 gramos

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Sinopsis

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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Excerpt from Computing Small Singular Values of Bidiagonal Matrices With Guaranteed High Relative Accuracy

Now we present our central result of this section (a slightly weaker version originally appeared in an unpublished report [kahan])

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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.

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