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Volume 42, Issue 4
A Trust-Region Method for Solving Truncated Complex Singular Value Decomposition

Jiaofen Li, Lingchang Kong, Xuefeng Duan, Xuelin Zhou & Qilun Luo

DOI: 10.4208/jcm.2211-m2021-0043

J. Comp. Math., 42 (2024), pp. 999-1031.

Published online: 2024-04

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  • 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.

  • Keywords

Truncated singular value decomposition, Riemannian optimization, Trust-region method.

  • AMS Subject Headings

15A24, 15A57, 65F10, 65F30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-42-999, author = {Li , JiaofenKong , LingchangDuan , XuefengZhou , Xuelin and Luo , Qilun}, 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 = {

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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2211-m2021-0043}, url = {http://global-sci.org/intro/article_detail/jcm/23044.html} }
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 -

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.

Jiaofen Li, Lingchang Kong, Xuefeng Duan, Xuelin Zhou & Qilun Luo. (2024). A Trust-Region Method for Solving Truncated Complex Singular Value Decomposition. Journal of Computational Mathematics. 42 (4). 999-1031. doi:10.4208/jcm.2211-m2021-0043
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