Updating Singular Value Decompositions. A Parallel Implementation.

Marc Moonen; Paul Van Dooren; Joos Vandewalle

doi:10.1117/12.962267

14 November 1989 Updating Singular Value Decompositions. A Parallel Implementation.

Marc Moonen, Paul Van Dooren, Joos Vandewalle

Proceedings Volume 1152, Advanced Algorithms and Architectures for Signal Processing IV; (1989) https://doi.org/10.1117/12.962267
Event: 33rd Annual Technical Symposium, 1989, San Diego, United States

Abstract

In this paper, we give an overview of a few recently obtained results regarding al-gorithms and systolic arrays for updating singular value decompositions. The Ordinary SVD as well as the Product SVD and the Quotient SVD will be discussed. The updating algorithms consist in an interlacing of QR-updatings and a Jacobi-type SVD-algorithm applied to the triangular factor(s). At any time step an approximate decomposition is computed from a previous approximation, with a limited number of operations (0 (n²)). When combined with exponential weighting, these algorithms are seen to be highly applicable to tracking probleths. Furthermore, they can elegantly be mapped onto systolic arrays, making use of slight modifications of well known systolic implementations for the matrix-vector product, the QR-updating and the SVD.

Citation Download Citation

Marc Moonen, Paul Van Dooren, and Joos Vandewalle "Updating Singular Value Decompositions. A Parallel Implementation.", Proc. SPIE 1152, Advanced Algorithms and Architectures for Signal Processing IV, (14 November 1989); https://doi.org/10.1117/12.962267

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