On parallel implementation of the one-sided Jacobi algorithm for singular value decompositions
نویسندگان
چکیده
In this paper we give evidence to show that in onesided Jacobi SVD computation the sorting of column norms in each sweep is very important. Two parallel Jacobi orderings are described. These orderings can generate n(n 1)=2 di erent index pairs and sort column norms at the same time. The one-sided Jacobi SVD algorithm using these parallel orderings converges in about the same number of sweeps as the sequential cyclic Jacobi algorithm. Some experimental results on a Fujitsu AP1000 are presented. The issue of equivalence of orderings is also discussed.
منابع مشابه
Dynamic Ordering for the Parallel One-sided Block-jacobi Svd Algorithm
The serial Jacobi algorithm (either one-sided or two-sided) for the computation of a singular value decomposition (SVD) of a general matrix has excellent numerical properties and parallelization potential, but it is considered to be the slowest method for computing the SVD. Even its parallelization with some parallel cyclic (static) ordering of subproblems does not lead to much improvement when...
متن کاملParallel Code for One-sided Jacobi-Method
One sided block Jacobi algorithm for the singular value decomposition (SVD) of matrix can be a method of choice to compute SVD efficiently and accurately in parallel. A given matrix is logically partitioned into block columns and is subjected to an iteration process. In each iteration step, for given two block columns, their Gram matrix is generated, its symmetric eigenvalue decomposition (EVD)...
متن کاملParallel One-Sided Block Jacobi SVD Algorithm: II. Implementation
This technical report is devoted to the description of implementation details of the accelerated parallel one-sided block Jacobi SVD algorithm, whose analysis and design was described in [21]. We provide discuss a suitable data layout for a parallel implementation of the algorithm on a parallel computer with distributed memory. This discussion is complicated by the fact that different computati...
متن کاملA Note on Multiplicative Backward Errors of Accurate SVD Algorithms
Multiplicative backward stability results are presented for two algorithms which compute the singular value decomposition of dense matrices. These algorithms are the classical onesided Jacobi algorithm, with a stringent stopping criterion, and an algorithm which uses one-sided Jacobi to compute high accurate singular value decompositions of matrices given as rank-revealing factorizations. When ...
متن کاملA Parallel Ring Ordering Algorithm for Eecient One-sided Jacobi Svd Computations
In this paper we give evidence to show that in one-sided Jacobi SVD computation the sorting of column norms in each sweep is very important. An eecient parallel ring Jacobi ordering for computing singular value decomposition is described. This ordering can generate n(n ? 1)=2 diierent index pairs and sort column norms at the same time. The one-sided Jacobi SVD algorithm using this parallel orde...
متن کامل