Acta mathematica scientia,Series A ›› 2022, Vol. 42 ›› Issue (6): 1898-1921.

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A Hybrid Algorithm for Solving Truncated Complex Singular Value Decomposition

Yuxin Zhang1,Wenting Hou1,Xuelin Zhou2,1,*(),Jiaofen Li1   

  1. 1 School of Mathematics and Computational Science, Center for Applied Mathematics of Guangxi(GUET), Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation, Guilin University of Electronic Technology, Guangxi Guilin 541004
    2 School of Mathematics and Statistics, Yunan University, Yunan Kunming 650000
  • Received:2021-06-19 Online:2022-12-26 Published:2022-12-16
  • Contact: Xuelin Zhou
  • Supported by:
    the National Natural Science Foundation(12261026);the National Natural Science Foundation(11961012);the National Natural Science Foundation(12201149);the Special Fund for Science and Technological Bases and Talents of Guangxi(2021AC06001);the Guangxi College Student Innovation and Entrepreneurship Training Program(201810595215);the GUET Graduate Innovation Project(2022YCXS142);the Guangxi Key Laboratory of Automatic Detecting Technology and Instruments(YQ21103);the Guangxi Key Laboratory of Automatic Detecting Technology and Instruments(YQ22106)


This paper develops an efficient approach for solving the truncated complex singular value decomposition, which is widely applied in ill-posed model problems. The original problem can be formulated as an optimization problem on a corresponding complex product Stiefel manifold. A hybrid Riemannian Newton-type algorithm with globally and quadratically convergent is proposed to solve the underlying problem, in which the involved Newton's equation is transformed into a standard symmetric linear system with a dimension reduction. Numerical experiments and detailed comparisons are provided to illustrate the efficiency of the proposed method.

Key words: Complex matrix, Truncated singular value decomposition, Riemannian Newton's method, Hybrid Algorithm

CLC Number: 

  • O151.1