Journal of Guangxi Normal University(Natural Science Edition) ›› 2022, Vol. 40 ›› Issue (4): 136-144.doi: 10.16088/j.issn.1001-6600.2021092301

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Rank Constraint Least Square Symmetric Semidefinite Solutions and Its Optimal Approximation of the Matrix Equation

YU Siting, PENG Jingjing*, PENG Zhenyun   

  1. College of Mathematics and Computer Science, Guilin University of Electronic Technology, Guilin Guangxi 541004,China
  • Published:2022-08-05

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Abstract: Based on the singular value decomposition and spectral decomposition of matrices, the necessary and sufficient conditions for the existence of solutions to rank constraint least square symmetric semidefinite solutions and itsoptimal approximation solution of the matrix equation AX=B are established and, if the solutions exist, the general expression of the solutions are proposed. The computational procedures of the optimal approximation solution, and the numerical examplesshowing the correctness of the theoretical results are given.

Key words: rank constraint matrix, matrix equation, symmetric semidefinite matrices, least square solution, optimal approximation

CLC Number: 

  • O151.21
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