Improving the Accuracy of Computed Singular Values
Jack J. Dongarra · SIAM Journal on Scientific and Statistical Computing · 1983
This paper describes a computational method for improving the accuracy of a given singular value and its associated left and right singular vectors. The method is analogous to iterative improvement for the solution of linear systems. That is, by means of a low-precision computation, an iterative algorithm is applied to increase the accuracy of the singular value and vectors; extended precision computations are used in the residual calculation. The method is related to Newton’s method applied to the singular value problem and inverse iteration for the eigenvalue problem.