On the convergence of the V-type hyperplane constrained method for singular value decomposition

Abstract

In this paper, we investigate the convergence of the V-type hyperplane constrained method for singular value decomposition. The V-type method involves employing the Newton type iteration to solve the nonlinear systems with the searching range of right singular vectors constrained on a hyperplane. First, we discuss the nonsingularity of the Jacobian matrix appearing in the Newton type iteration. Next, we clarify the convergence of the Newton type iteration. Finally, we prove that singular value decomposition is computable by the V-type method.