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Accurate singular values and differential qd algorithms. (English) Zbl 0814.65036
An algorithm to compute the singular values of a bidiagonal matrix based on the quotient difference algorithm by 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 J. Demmel and W. Kahan [SIAM J. Sci. Stat. Comput. 11, No. 5, 873-912 (1990; Zbl 0705.65027)].

MSC:
65F15 Numerical computation of eigenvalues and eigenvectors of matrices
65Y05 Parallel numerical computation
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