Updating Singular Value Decompositions. A Parallel Implementation.
Marc Moonen, Paul Van Dooren, Joos P. L. Vandewalle · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1989
AbstractIn 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 Q^-upd&tings 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 (O(n2 )). When combined with exponential weighting, these algorithms are seen to be highly applicable to tracking problems. 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 Q^-updating and the SVD. 1 Introduction Let A be an m x n matrix, with (m > n). The Ordinary Singular Value Decomposition (OSVD) is a factorization of A into a product of three matriceswhere £/*[/ = I, V*V = I, and S is a diagonal matrix, with the singular values on the main The updating problem considered here, consists in computing the OSVD of the modified matrix[ \.A ] _ ^ ^ a1 \-U(