Computing Small Singular Values of Bidiagonal Matrices With Guaranteed High

James Demmel, W. Kahan

ISBN 10: 1332870732 / ISBN 13: 9781332870738

Editore: Forgotten Books, 2018

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Print on Demand. 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. 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.

Codice articolo 9781332870738_0

Dati bibliografici

• Titolo: Computing Small Singular Values of Bidiagonal Matrices With Guaranteed High
• Editore: Forgotten Books
• Data di pubblicazione: 2018
• Lingua: Inglese
• ISBN 10: 1332870732
• ISBN 13: 9781332870738
• Rilegatura: Paperback
• Condizione: New
• Tipo di libro: print-on-demand item
• Cataloghi dei venditori:
  • Calculus

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Riassunto

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.