A TRUST-REGION METHOD FOR SOLVING TRUNCATED COMPLEX SINGULAR VALUE DECOMPOSITION  

作　　者：Jiaofen Li Lingchang Kong Xuefeng Duan Xuelin Zhou Qilun Luo 

机构地区：[1]School of Mathematics and Computing Science,Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation,Guangxi Key Laboratory of Automatic Detecting Technology and Instruments,Guilin University of Electronic Technology,Center for Applied Mathematics of Guangxi(GUET),Guilin 541004,China [2]School of Mathematical Sciences,South China Normal University,Guangzhou 510000,China [3]School of Mathematics and Computing Science,Guilin University of Electronic Technology,Guilin 541004,China [4]School of Mathematics and Computing Science,Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation,Guilin University of Electronic Technology,Center for Applied Mathematics of Guangxi(GUET),Guilin 541004,China [5]School of Mathematics and Statistics,Yunan University,Kunming 650000,China

出　　处：《Journal of Computational Mathematics》2024年第4期999-1031,共33页计算数学（英文）

基　　金：supported by the National Natural Science Foundation of China(Grant Nos.12261026,11961012,12201149);by the Natural Science Foundation of Guangxi Province(Grant Nos.2016GXNSFAA380074,2023GXNSFAA026067);by the Innovation Project of GUET Graduate Education(Grant No.2022YXW01);by the GUET Graduate Innovation Project(Grant No.2022YCXS142);by the Guangxi Key Laboratory of Automatic Detecting Technology and Instruments(Grant Nos.YQ23103,YQ21103,YQ22106);by the Special Fund for Science and Technological Bases and Talents of Guangxi(Grant No.2021AC06001);by the Guizhou Science and Technology Program of Projects(Grant No.ZK2021G339)。

摘　　要：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 optimiza-tion 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 conver-gence 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.

关 键 词：Truncated singular value decomposition Riemannian optimization Trust-region method 

分 类 号：O18[理学—数学]