An application of the Kato-Temple inequality on matrix eigenvalues to the dqds algorithm for singular values

抄録

Choice of suitable shifts strongly influences performance of numerical algorithms with shift for computing matrix eigenvalues or singular values. On the dqds (differential quotient difference with shifts) algorithm for singular values, a new shift strategy is proposed in this paper. The new shift strategy includes shifts obtained from an application of the Kato-Temple inequality on matrix eigenvalues. The dqds algorithm with the new shift strategy is shown to have a better performance in iteration number than that of the subroutine DLASQ in LAPACK.