Quadratic convergence of a special quasi-cyclic Jacobi method

摘要

This paper considers the ultimate asymptotic convergence of a block- oriented, quasi-cyclic Jacobi method for symmetric matrices. The conclusion applies to the new one-sided Jacobi method for computing the singular value decomposition, recently proposed by Drmač and Veselić. Using a simple qualitative analysis, the discussion indicates that a quadratic off-norm reduction per quasi-sweep is to be expected in all perceivable cases.