Accurate singular values and differential qd algorithms (Q1326368)

An algorithm to compute the singular values of a bidiagonal matrix based on the quotient difference algorithm by \textit{H. Rutishauser} [Z. Angew. Math. Phys. 5, 233-251 (1954; Zbl 0055.347)] is studied. It is implemented using neither square roots nor subtractions and gives high relative accuracy for small singular values, is very fast and can be implemented in parallel. Comparisons are made to the recent algorithm by \textit{J. Demmel} and \textit{W. Kahan} [SIAM J. Sci. Stat. Comput. 11, No. 5, 873-912 (1990; Zbl 0705.65027)].