The Bidiagonal Singular Value Decomposition and Hamiltonian Mechanics (Classic Reprint) - Couverture souple
Synopsis
Understanding how precision and structure shape fast, reliable SVD computations This book explains how focusing on bidiagonal matrices yields much higher accuracy in singular value computations and how a Hamiltonian flow underpins a stable algorithm.
The work frames a practical problem: computing singular values and vectors with high relative accuracy, even when data are imperfect. It connects theory to algorithm design, showing how a zero-shift QR approach and careful stopping criteria preserve essential structure and minimize error growth. Readers will see how mathematical insights translate into robust numerical methods with real-world impact.
- How relative, not absolute, perturbations affect singular values and vectors in bidiagonal matrices
- How a Hamiltonian differential equation helps analyze and bound rounding errors
- How a hybrid QR algorithm achieves high accuracy while staying fast
- How to interpret algorithm behavior through a structured, tree-based error analysis
Ideal for readers of technical math and numerical analysis, this edition is a practical guide to understanding the limits and capabilities of modern SVD algorithms. It is especially relevant for anyone applying eigenvalue or singular value methods to large or delicate problems.
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The Bidiagonal Singular Value Decomposition and Hamiltonian Mechanics
impression à la demandeVendeur : Forgotten Books, London, Royaume-Uni
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Paperback. Etat : New. Print on Demand. This book delves into the complex world of singular value decomposition (SVD), a fundamental mathematical operation used to analyze matrices. It examines the process of computing the SVD of a bidiagonal matrix, a specific type of matrix that arises in various applications, including the SVD of general matrices and the eigenproblem of symmetric tridiagonal matrices. The author's exploration of this topic builds upon existing research in the field, particularly the work of Demmel and Kahan, and presents new insights regarding the accuracy of SVD computations. The book's core theme revolves around demonstrating that SVD calculations on bidiagonal matrices can achieve significantly higher accuracy than those performed on general matrices. This unexpected result stems from the nature of bidiagonal matrices, where relative errors in the entries lead to relative errors in the singular values, unlike in general matrices where absolute errors are dominant. Furthermore, the book introduces a novel Hamiltonian approach to analyze the algorithm used for SVD calculations. This approach, drawing upon the concepts of Hamiltonian mechanics, reveals a deeper understanding of how errors propagate during the computation process. The book's exploration of Hamiltonian mechanics and its application to the SVD algorithm offers a new paradigm for developing high-accuracy algorithms for solving other eigenvalue problems. 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. N° de réf. du vendeur 9781334196904_0
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The Bidiagonal Singular Value Decomposition and Hamiltonian Mechanics Classic Reprint
Vendeur : PBShop.store US, Wood Dale, IL, Etats-Unis
Évaluation du vendeur 5 sur 5 étoiles
PAP. Etat : New. New Book. Shipped from UK. Established seller since 2000. N° de réf. du vendeur LW-9781334196904
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EUR 25,50
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Expédition nationale : Etats-Unis
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The Bidiagonal Singular Value Decomposition and Hamiltonian Mechanics Classic Reprint
Vendeur : PBShop.store UK, Fairford, GLOS, Royaume-Uni
Évaluation du vendeur 5 sur 5 étoiles
PAP. Etat : New. New Book. Shipped from UK. Established seller since 2000. N° de réf. du vendeur LW-9781334196904
Acheter neuf
EUR 25,08
Expédition à EUR 3,86
Expédition depuis Royaume-Uni vers Etats-Unis
Expédition depuis Royaume-Uni vers Etats-Unis
Quantité disponible : 15 disponible(s)