On the Error Analysis and Implementation of Some Eigenvalue Decomposition and Singular Value Decomposition Algorithms

Authors:
Huan Ren
Affiliations:
-
Venue:
On the Error Analysis and Implementation of Some Eigenvalue Decomposition and Singular Value Decomposition Algorithms
Year:
1997

Citing 0
Cited 1

On the estimation of numerical error bounds in linear algebra based on discrete stochastic arithmetic

Applied Numerical Mathematics

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Abstract

Many algorithms exist for computing the symmetric eigendecomposition, the singular value decomposition and the generalized singular value decomposition. In this thesis, we present several new algorithms and improvements on old algorithms, analyzing them with respect to their speed, accuracy, and storage requirements. We first discuss the variations on the bisection algorithm for finding eigenvalues of symmetric tridiagonal matrices. We then discuss a fast implementation of bisection using parallel prefix. We also discuss possible ways to stabilize it by using iterative refinement. Finally, we discuss how to use a divide-and-conquer algorithm to compute the singular value decomposition and solve the linear least squares problem and how to implement Van Loan''s algorithm for the generalized singular value decomposition using the divide-and-conquer algorithm.