@Article{JCM-42-4,
author = {Li, Jiaofen and Lingchang, Kong and Xuefeng, Duan and Zhou, Xuelin and Qilun, Luo},
title = {A Trust-Region Method for Solving Truncated Complex Singular Value Decomposition},
journal = {Journal of Computational Mathematics},
year = {2024},
volume = {42},
number = {4},
pages = {999--1031},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {1991-7139},
doi = {https://doi.org/10.4208/jcm.2211-m2021-0043},
url = {https://global-sci.com/article/91086/a-trust-region-method-for-solving-truncated-complex-singular-value-decomposition}
}