Computing Small Singular Values of Bidiagonal Matrices With Guaranteed High Relative Accuracy (Classic Reprint) - Softcover
Synopsis
High-precision singular values for bidiagonal matrices, with a faster, stable algorithm. A new approach blends the standard QR iteration with a zero-shift variant to guarantee forward stability and high relative accuracy for all singular values, regardless of their size.
This book presents the theory and the algorithm, showing how small relative changes in the data lead to small relative changes in the singular values. It also explains how the method can be used to compute eigenvalues of symmetric tridiagonal matrices and discusses convergence criteria, practical implementation details, and numerical results that compare performance with traditional methods.
- How a QR-based algorithm can achieve guaranteed high relative accuracy for every singular value of a bidiagonal matrix.
- Conditions and perturbation results that justify stability and accurate results across a range of matrix structures.
- The role of a forward-stable, zero-shift modification to the QR iteration and its practical impact on speed.
- Numerical experiments and practical considerations, including when and how the method outperforms standard approaches.
Ideal for readers of numerical linear algebra and computational mathematics seeking robust, precision-focused methods for singular value and eigenvalue problems.
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Computing Small Singular Values of Bidiagonal Matrices With Guaranteed High
Print on DemandSeller: Forgotten Books, London, United Kingdom
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Paperback. Condition: New. 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. print-on-demand item. Seller Inventory # 9781332870738_0
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Computing Small Singular Values of Bidiagonal Matrices With Guaranteed High Relative Accuracy Classic Reprint
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PAP. Condition: New. New Book. Shipped from UK. Established seller since 2000. Seller Inventory # LW-9781332870738
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Computing Small Singular Values of Bidiagonal Matrices With Guaranteed High Relative Accuracy Classic Reprint
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PAP. Condition: New. New Book. Shipped from UK. Established seller since 2000. Seller Inventory # LW-9781332870738
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