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首页> 美国政府科技报告 >Computing Small Singular Values of Bidiagonal Matrices with Guaranteed High Relative Accuracy: LAPACK Working Note Number 3
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Computing Small Singular Values of Bidiagonal Matrices with Guaranteed High Relative Accuracy: LAPACK Working Note Number 3

机译：计算具有保证的高相对精度的双对角矩阵的小奇异值：LapaCK工作注3号

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摘要

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. We present a new algorithm which computes all the singular values of a bidiagonal matrix to high relative accuracy independent of their magnitudes. 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. We also show how to accurately compute tiny eigenvalues of some classes of symmetric tridiagonal matrices using the same technique. 11 refs., 4 tabs.

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