Parallel SVD updating using approximate rotations

Juergen Goetze; Peter Rieder; J. A. Nossek

doi:10.1117/12.211402

7 June 1995 Parallel SVD updating using approximate rotations

Juergen Goetze, Peter Rieder, J. A. Nossek

Proceedings Volume 2563, Advanced Signal Processing Algorithms; (1995) https://doi.org/10.1117/12.211402
Event: SPIE's 1995 International Symposium on Optical Science, Engineering, and Instrumentation, 1995, San Diego, CA, United States

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.

Citation Download Citation

Juergen Goetze, Peter Rieder, and J. A. Nossek "Parallel SVD updating using approximate rotations", Proc. SPIE 2563, Advanced Signal Processing Algorithms, (7 June 1995); https://doi.org/10.1117/12.211402

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