The algebraic eigenvalue problem
The algebraic eigenvalue problem
Applied numerical linear algebra
Applied numerical linear algebra
Data structures for weighted matching and nearest common ancestors with linking
SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
LAPACK Users' guide (third ed.)
LAPACK Users' guide (third ed.)
Handbook of Theoretical Computer Science
Handbook of Theoretical Computer Science
Computing Minimum-Weight Perfect Matchings
INFORMS Journal on Computing
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
On variable blocking factor in a parallel dynamic block: Jacobi SVD algorithm
Parallel Computing - Parallel matrix algorithms and applications (PMAA '02)
Accelerating the SVD Block-Jacobi Method
Computing - Editorial: Special issue on GAMM – Workshop on Guaranteed Error-bounds for the Solution of Nonlinear Problems in Applied Mathematics
Efficient pre-processing in the parallel block-Jacobi SVD algorithm
Parallel Computing - Parallel matrix algorithms and applications (PMAA'04)
Distributed Jacobi joint diagonalization on clusters of personal computers
International Journal of Parallel Programming
A relaxation scheme for increasing the parallelism in Jacobi-SVD
Journal of Parallel and Distributed Computing
On iterative QR pre-processing in the parallel block-Jacobi SVD algorithm
Parallel Computing
A novel scheme for the parallel computation of SVDs
HPCC'06 Proceedings of the Second international conference on High Performance Computing and Communications
A block JRS algorithm for highly parallel computation of SVDs
HPCC'07 Proceedings of the Third international conference on High Performance Computing and Communications
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A new approach for the parallel computation of singular value decomposition (SVD) of matrix A ∈ Cm×n is proposed. Contrary to the known algorithms that use a static cyclic ordering of subproblems simultaneously solved in one iteration step, the proposed implementation of the two-sided block-Jacobi method uses a dynamic ordering of subproblems. The dynamic ordering takes into account the actual status of matrix A. In each iteration step, a set of the off-diagonal blocks is determined that reduces the Frobenius norm of the off-diagonal elements of A as much as possible and, at the same time, can be annihilated concurrently. The solution of this task is equivalent to the solution of the maximum-weight perfect matching problem. The greedy algorithm for the efficient solution of this problem is presented. The computational experiments with both types of ordering, incorporated into the two-sided block-Jacobi method, were performed on an SGI - Cray Origin 2000 parallel computer using the Message Passing Interface (MPI). The results confirm that the dynamic ordering is much more efficient with regard to the amount of work required for the computation of SVD of a given accuracy than the static cyclic ordering.