The Bidiagonal Singular Value Decomposition and Hamiltonian Mechanics
- 1 October 1991
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Numerical Analysis
- Vol. 28 (5) , 1463-1516
- https://doi.org/10.1137/0728076
Abstract
We consider computing the singular value decomposition of a bidiagonal matrix B. Thisproblem arises in the singular value decomposition of a general matrix, and in the eigenproblemfor a symmetric positive definite tridiagonal matrix. We show that if the entries ofB are known with high relative accuracy, the singular values and singular vectors of B willbe determined to much higher accuracy than the standard perturbation theory suggests.We also show that the algorithm in [Demmel and Kahan] ...Keywords
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