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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 relativedoi:10.1137/0911052 fatcat:vzin6vxuybex5fjfskzwlftbby