Bidiagonalization and diagonalization

Adaptive Parallel Householder Bidiagonalization

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....

Bidiagonalization with Parallel Tiled Algorithms

We consider algorithms for going from a “full” matrix to a condensed “band bidiagonal” form using orthogonal transformations. We use the framework of “algorithms by tiles”. Within this framework, we study: (i) the tiled bidiagonalization algorithm BiDiag, which is a tiled version of the standard scalar bidiagonalization algorithm; and (ii) the R-bidiagonalization algorithm R-BiDiag, which is a ...

Lanczos Bidiagonalization With Partial Reorthogonalization

Bidiagonalization and symmetric tridiagonalization by systolic arrays

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...

Generalized Golub-Kahan Bidiagonalization and Stopping Criteria

The Golub–Kahan bidiagonalization algorithm has been widely used in solving leastsquares problems and in the computation of the SVD of rectangular matrices. Here we propose an algorithm based on the Golub–Kahan process for the solution of augmented systems that minimizes the norm of the error and, in particular, we propose a novel estimator of the error similar to the one proposed by Hestenes a...