Updating Singular Value Decompositions. A Parallel Implementation.

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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.

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