Computing small singular values of bidiagonal matrices with guaranteed high relative accuracy: LAPACK working note number 3
J. Demmel, W. Kahan · OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) · 1988
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.