ACCURATE SINGULAR-VALUES OF BIDIAGONAL MATRICES
ACCURATE SINGULAR-VALUES OF BIDIAGONAL MATRICES
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DOI：
10.1137/0911052
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发表时间：
1990-09-01
期刊：
影响因子：
--
通讯作者：
KAHAN, W
中科院分区：
文献类型：
--
作者：
DEMMEL, J;KAHAN, W
计算双对角矩阵的奇异值是一般矩阵奇异值分解的标准算法的最后阶段。本文提出了一种新的算法，它能以较高的相对精度计算双对角矩阵的所有奇异值，而与奇异值的大小无关。相比之下，双对角矩阵的标准算法可以计算小的奇异值，而根本没有相对精度。数值实验表明，新算法在速度上与标准算法相当，而且往往更快。
Computing the singular values of a bidiagonal matrix is the final phase of the standard algorithm for the singular value decomposition of a general matrix. A new algorithm that computes all the singular values of a bidiagonal matrix to high relative accuracy independent of their magnitudes is presented. In contrast, the standard algorithm for bidiagonal matrices may compute small singular values with no relative accuracy at all. Numerical experiments show that the new algorithm is comparable in speed to the standard algorithm, and frequently faster.