A posteriori computation of the singular vectors in a preconditioned Jacobi SVD algorithm

This paper describes a novel way to implement the Jacobi algorithm for the singular value decomposition of full rank matrices. It is shown that the left and right singular vectors can be computed without explicit accumulation of Jacobi rotations. Instead, the accumulated product of Jacobi rotations is computed a posteriori as the solution of a certain well-conditioned matrix equation. Theoretical analysis provides tools to estimate, check and, if necessary, to improve the accuracy of the computed decomposition. Experimental results show that the new technique performs very well in practice.