TY - JOUR
T1 - A Trust-Region Method for Solving Truncated Complex Singular Value Decomposition
AU - Li , Jiaofen
AU - Kong , Lingchang
AU - Duan , Xuefeng
AU - Zhou , Xuelin
AU - Luo , Qilun
JO - Journal of Computational Mathematics
VL - 4
SP - 999
EP - 1031
PY - 2024
DA - 2024/04
SN - 42
DO - http://doi.org/10.4208/jcm.2211-m2021-0043
UR - https://global-sci.org/intro/article_detail/jcm/23044.html
KW - Truncated singular value decomposition, Riemannian optimization, Trust-region method.
AB - <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>