We give a systolic algorithm and array for bidiagonalization of an n x n matrix in O(nlog, n) time, using O(n2) cells. Bandedness of the input matrix may be effectively exploited. If the matrix is banded, with p nonzero subdiagonals and q nonzero superdiagonais, then 4n In(p + q) + O(n) clocks and 2n(p + q ) + O((p + q)’ + n) cells are needed. This is faster than the best previously reported re...

For the accurate approximation of the minimal singular triple (singular value and left and right singular vector), we may use two separate search spaces, one for the left, and one for the right singular vector. In Lanczos bidiagonalization, for example, such search spaces are constructed. In [3], the author proposes a Jacobi–Davidson type method for the singular value problem, where solutions t...

With the increasing use of high-resolution multimedia streams and large image and video archives in many of today’s research and application areas, there is a growing need for multimedia-oriented highperformance computing. As a consequence, a need for algorithms, methodologies, and tools that can serve as support in the (automatic) parallelization of multimedia applications is rapidly emerging....

A matrix-free algorithm, IRLANB, for the efficient computation of the smallest singular triplets of large and possibly sparse matrices is described. Key characteristics of the approach are its use of Lanczos bidiagonalization, implicit restarting, and harmonic Ritz values. The algorithm also uses a deflation strategy that can be applied directly on Lanczos bidiagonalization. A refinement postpr...

Low-rank approximation of large and/or sparse matrices is important in many applications, and the singular value decomposition (SVD) gives the best low-rank approximations with respect to unitarily-invariant norms. In this paper we show that good low-rank approximations can be directly obtained from the Lanczos bidiagonalization process applied to the given matrix without computing any SVD. We ...