Accurate Singular Values of Bidiagonal Matrices
SIAM J. Sci. Stat. Comput, (1990)Abstract
omputing the singular values of a bidiagonal matrix is the fin al phase of the standard algow rithm for the singular value decomposition of a general matrix. We present a new algorithm hich compu tes all the singular values of a bidiagonal matrix to high relative accuracy indepen- - p den t of their magn itudes. In contrast, the standard algorithm for bidiagonal matrices may com ute sm all singular values with no relative accuracy at all. Numerical experiments show that K the new algorithm is comparable in speed to the standard algorithm , and frequently faster. eywords: singular value decomposition , bidiagonal matrix, QR iteration 1 AMS(MOS) subject classifications: 65F20, 65G05, 65F35 . Introduction The standard algorithm for computing the singular value decomposition ( SVD ) of a gen1 eral real matrix A has two phases 7: ) Compute orthogonal matrices P and Q such that B = P AQ is in bidiagonal form , i.e. 1 1 1 T 1 . 2 has nonzero en tries only on its diagonal and first su...
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