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Dynamic ordering for a parallel block-Jacobi SVD algorithm

机译:并行块-Jacobi SVD算法的动态排序

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摘要

A new approach for the parallel computation of singular value decomposition(SVD) of matrix A ∈C~m X n is proposed. Contrary to the known algorithms that use a static cyclic order- ing of subproblems simultaneously solved in one iteration step, the proposed implementation of the two-sided block-Jacobi method uses a dynamic ordering of subprodblems. 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.
机译:提出了一种并行计算矩阵A∈C〜m X n的奇异值分解的新方法。与在一个迭代步骤中同时解决的使用子问题的静态循环排序的已知算法相反,所提出的双面块-雅可比方法的实现方式使用子问题的动态排序。动态排序考虑了矩阵A的实际状态。在每个迭代步骤中,确定一组偏离对角的块,这些块尽可能地减小A的偏离对角元素的Frobenius范数时间,可以同时消灭。

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