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Proceedings Paper

Parallel SVD updating using approximate rotations
Author(s): Juergen Goetze; Peter Rieder; J. A. Nossek
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Paper Abstract

In this paper a parallel implementation of the SVD-updating algorithm using approximate rotations is presented. In its original form the SVD-updating algorithm had numerical problems if no reorthogonalization steps were applied. Representing the orthogonalmatrix V (right singular vectors) using its parameterization in terms of the rotation angles of n(n - 1)/2 plane rotations these reorthogonalization steps can be avoided during the SVD-updating algorithm. This results in a SVD-updating algorithm where all computations (matrix vector multiplication, QRD-updating, Kogbetliantz's algorithm) are entirely based on the evaluation and application of orthogonal plane rotations. Therefore, in this form the SVD-updating algorithm is amenable to an implementation using CORDIC-based approximate rotations. Using CORDIC-based approximate rotations the n(n - 1)/2 rotations representing V (as well as all other rotations) are only computed to a certain approximation accuracy (in the basis arctan 2i). All necessary computations required during the SVD-updating algorithm (exclusively rotations) are executed with the same accuracy, i.e., only r << w (w: wordlength) elementary orthonormal (mu) rotations are used per plane rotation. Simulations show the efficiency of the implementation using CORDIC-based approximate rotations.

Paper Details

Date Published: 7 June 1995
PDF: 11 pages
Proc. SPIE 2563, Advanced Signal Processing Algorithms, (7 June 1995); doi: 10.1117/12.211402
Show Author Affiliations
Juergen Goetze, Rice Univ. (United States)
Peter Rieder, Technische Univ. Muenchen (Germany)
J. A. Nossek, Technische Univ. Muenchen (Germany)


Published in SPIE Proceedings Vol. 2563:
Advanced Signal Processing Algorithms
Franklin T. Luk, Editor(s)

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