Parallel algorithms for singular value decomposition

Includes bibliographical references.In motion rate control applications, it is faster and easier to solve the equations involved if the singular value decomposition (SVD) of the Jacobian matrix is first determined. A parallel SVD algorithm with minimum execution time is desired. One approach using Givens rotations lends itself to parallelization, reduces the iterative nature of the algorithm, and efficiently handles rectangular matrices. This research focuses on the minimization of the SVD execution time when using this approach. Specific issues addressed include considerations of data mapping, effects of the number of processors used on execution time, impacts of the interconnection network on performance, and trade-offs between modes of parallelism. Results are verified by experimental data collected on the PASM parallel machine prototype.This research was supported in part by the National Science Foundation under grant CDA-9015696, by Sandia National Laboratories under contract 18-4379B, and by Rome Laboratory under contract F30602-94-C-0022

Parallel approaches for singular value decomposition as applied to robotic manipulator Jacobians

Includes bibliographical references (pages 33-35).The system of equations that govern kinematically redundant robotic manipulators is commonly solved by finding the singular value decomposition (SVD) of the corresponding Jacobian matrix. This can require a considerable amount of time to compute, thus a parallel SVD algorithm reducing execution time is sought. The approach employed here lends itself to parallelization by using Givens rotations and information from previous decompositions. The key contribution of this research is the presentation and implementation of parallel SVD algorithms to compute the SVD for a set of Jacobians that represent various different joint failure scenarios. Results from implementation of the algorithm on a MasPar MP-1, an IBM SP2, and the PASM prototype parallel computers are compared. Specific issues considered for each implementation include: how data is mapped to the processing elements, the effect that increasing the number of processing elements has on execution time, the type of parallel architecture used, and trade-offs between modes of parallelism