Accurate Singular Values of Bidiagonal Matrices

James Demmel, W. Kahan
1990 SIAM Journal on Scientific and Statistical Computing  
C Jam es D em m el W. Kah an ouran t Institute C Abstract om puting the singular valu es of a bidiagonal m atrix is the fin al phase of the stan dard algow rithm for the singular valu e decom position of a general m atrix. We present a new algorithm hich com putes all the singular valu es of a bidiagonal m atrix to high relative accuracy indepen-p dent of their m agn itudes. In contrast, the stan dard algorithm for bidiagonal m atrices m ay com ute sm all singular valu es with no relative
more » ... h no relative accuracy at all. Num erical experim ents sh ow that K the new algorithm is com parable in speed to the stan dard algorithm , an d frequently faster. eywords: singular valu e decom position, bidiagonal m atrix, QR iteration 1 AMS( MOS) subject classifications: 65F20, 65G 05, 65F35
doi:10.1137/0911052 fatcat:vzin6vxuybex5fjfskzwlftbby