The design and analysis of parallel algorithms
The design and analysis of parallel algorithms
SIAM Journal on Scientific and Statistical Computing
On the convergence of the cyclic Jacobi method for parallel block orderings
SIAM Journal on Matrix Analysis and Applications
An Improved Algorithm for Computing the Singular Value Decomposition
ACM Transactions on Mathematical Software (TOMS)
Computing the Singular Value Decomposition on a Distributed System of Vector Processors
Computing the Singular Value Decomposition on a Distributed System of Vector Processors
Systolic block-Jacobi SVD algorithm for processor meshes
Highly parallel computaions
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The paper ' presents parallel algorithms for eflcient solution of the SVD (Singular Value Decomposition) problem by the block two-sided Jacobi method. It is shown how the method could be applied to MIMD computers with the hypercube and ring topology. Three types of orderings for solving SVD on block-structured submatrices are analysed from the point of view of communication requirements and suitability for a parallel execution of the computationalprocess. which is carried out on block-columns of the matrix. All three orderings fit well to the hypercube topology. Two of them can be directly implemented also on rings. The optimality in parallelization of the method and data transfers has been achieved there within each sweep. For the third scheme, an eficient numbering of processor nodes is discussed. Computer results obtained on an Intel Paragon system are shown for a chosen ordering.