A TRUST-REGION METHOD FOR SOLVING TRUNCATED COMPLEX SINGULAR VALUE DECOMPOSITION
作者机构：School of Mathematics and Computing ScienceGuangxi Colleges and Universities Key Laboratory of Data Analysis and ComputationGuangxi Key Laboratory of Automatic Detecting Technology and InstrumentsGuilin University of Electronic TechnologyCenter for Applied Mathematics of Guangxi(GUET)Guilin 541004China School of Mathematical SciencesSouth China Normal UniversityGuangzhou 510000China School of Mathematics and Computing ScienceGuilin University of Electronic TechnologyGuilin 541004China School of Mathematics and Computing ScienceGuangxi Colleges and Universities Key Laboratory of Data Analysis and ComputationGuilin University of Electronic TechnologyCenter for Applied Mathematics of Guangxi(GUET)Guilin 541004China School of Mathematics and StatisticsYunan UniversityKunming 650000China
出 版 物：《Journal of Computational Mathematics》 (计算数学（英文）)
年 卷 期：2024年第42卷第4期
页 面：999-1031页
核心收录：
学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学]
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)
主 题：Truncated singular value decomposition Riemannian optimization Trust-region method
摘 要：The truncated singular value decomposition has been widely used in many areas of science including engineering,and statistics,*** 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 *** presented to solve the underlying problem,which enjoys the global convergence and local superlinear conver-gence *** experiments are provided to illustrate the efficiency of the proposed *** 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.
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