On one-sided Jacobi methods for parallel computation
On one-sided Jacobi methods for parallel computation
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DOI：
10.1137/0608064
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发表时间：
1987-10
期刊：
影响因子：
--
通讯作者：
P. Eberlein
中科院分区：
文献类型：
--
作者：
P. Eberlein
给出了求解奇异值问题的单边Jacobi/Hestenes方法的收敛性证明。导出了Hestenes法在原矩阵为正态时矩阵迭代的极限形式；这个极限矩阵是块对角矩阵，其中块是酉矩阵的倍数。对于对称特征值问题，给出了保证收敛到对角矩阵的算法的一个变化。指出了并行计算的实现技术，特别是在超立方体上的实现技术。
Convergence proofs are given for one-sided Jacobi/Hestenes methods for the singular value problem. The limiting form of the matrix iterates for the Hestenes method with optimization when the original matrix is normal is derived; this limiting matrix is block diagonal, where the blocks are multiples of unitary matrices. A variation in the algorithm to guarantee convergence to a diagonal matrix for the symmetric eigenvalue problem is shown. Implementation techniques for parallel computation, in particular, on the hypercube are indicated.