A Trust-Region Method for Solving Truncated Complex Singular Value Decomposition

Abstract

The truncated singular value decomposition has been widely used in many areas of science including engineering, and statistics, etc. In this paper, the original truncated complex singular value decomposition problem is formulated as a Riemannian optimization problem on a product of two complex Stiefel manifolds, a practical algorithm based on the generic Riemannian trust-region method of Absil et al. is presented to solve the underlying problem, which enjoys the global convergence and local superlinear convergence rate. Numerical experiments are provided to illustrate the efficiency of the proposed method. Comparisons with some classical Riemannian gradient-type methods, the existing Riemannian version of limited-memory BFGS algorithms in the MATLAB toolbox Manopt and the Riemannian manifold optimization library ROPTLIB, and some latest infeasible methods for solving manifold optimization problems, are also provided to show the merits of the proposed approach.