Block-SVD algorithms and their adaptation to hypercubes and rings

The paper presents parallel algorithms for efficient 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 computational process, 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 efficient numbering of processor nodes is discussed. Computer results obtained on an Intel Paragon system are shown for a chosen ordering.