A survey on convergence theorems of the dqds algorithm for computing singular values

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Abstract

This is a survey on convergence theorems for the differential quotient difference with shifts (dqds) algorithm, which is one of the most efficient methods for computing matrix singular values. Emphasis is laid on the relationship and comparison between the global convergence theorem obtained recently by the present authors and Rutishauser’s convergence theorem for the Cholesky LR method with shifts for the positive-definite eigenvalue problem. Theorems on convergence rate of the dqds algorithm with different shift strategies are also reviewed.

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