A Trust-Region Method for Solving Truncated Complex Singular Value Decomposition (Journal of Computational Mathematics, 2024)
The truncated singular value decomposition has been widely used in many areas ofscience including engineering, and statistics, etc. In this paper, the original truncatedcomplex singular value decomposition problem is formulated as a Riemannian optimization problem on a product of two complex Stiefel manifolds, a practical algorithm basedon the generic Riemannian trust-region method of Absil et al. is presented to solve theunderlying problem, which enjoys the global convergence and local superlinear convergence rate. Numerical experiments are provided to illustrate the efficiency of the proposedmethod. Comparisons with some classical Riemannian gradient-type methods, the existingRiemannian version of limited-memory BFGS algorithms in the MATLAB toolbox Manoptand the Riemannian manifold optimization library ROPTLIB, and some latest infeasiblemethods for solving manifold optimization problems, are also provided to show the meritsof the proposed approach.