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Fast polar decomposition of an arbitrary matrix (1990)
| Venue: | SIAM J. Sci. Statist. Comput |
| Citations: | 40 - 8 self |
BibTeX
@ARTICLE{Higham90fastpolar,
author = {Nicholas J. Higham and Robert S. Schreiber and Mims Eprint and Nicholas J. Higham and Robert and S. Schreiber},
title = {Fast polar decomposition of an arbitrary matrix},
journal = {SIAM J. Sci. Statist. Comput},
year = {1990}
}
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Abstract
Abstract. The polar decomposition of an m x n matrix A of full rank, where rn n, can be computed using a quadratically convergent algorithm of Higham SIAMJ. Sci. Statist. Comput., 7 (1986), pp. 1160-1174]. The algorithm is based on a Newton iteration involving a matrix inverse. It is shown how, with the use of a preliminary complete orthogonal decomposition, the algorithm can be extended to arbitrary A. The use of the algorithm to compute the positive semidefinite square root of a Hermitian positive semidefinite matrix is also described. A hybrid algorithm that adaptively switches from the matrix inversion based iteration to a matrix multiplication based iteration due to Kovarik, and to Bj6rck and Bowie, is formulated. The decision when to switch is made using a condition estimator. This "matrix multiplication rich " algorithm is shown to be more efficient on machines for which matrix multiplication can be executed 1.5 times faster than matrix inversion. Key words, polar decomposition, complete orthogonal decomposition, matrix square root, matrix multiplication, Schulz iteration, condition estimator AMS(MOS) subject classification.
Keyphrases
matrix multiplication arbitrary matrix fast polar decomposition matrix inversion polar decomposition matrix multiplication rich algorithm subject classification condition estimator am schulz iteration positive semidefinite square root key word preliminary complete orthogonal decomposition matrix inverse hermitian positive semidefinite matrix full rank square root hybrid algorithm condition estimator higham siamj complete orthogonal decomposition convergent algorithm newton iteration
