journal6 ›› 2015, Vol. 36 ›› Issue (3): 1-6.DOI: 10.3969/j.cnki.jdxb.2015.03.001

• Mathematics •     Next Articles

An Orthogonal Projection Iteration Method for a Matrix Equations

ZHOU  Fu-Zhao, TIAN  Shi-Yu, YUAN  Yan-Jie   

  1. (College of Mathematics and Computing Science,Changsha University of Science and Technology,Changsha 410004,China)
  • Online:2015-05-25 Published:2015-06-03

Abstract: An orthogonal projection iteration method for matrix equations AX=B,XC=D is studied.Firstly,the iterative method is constructed by using the theory of orthogonal projection and the properties of general matrix;secondly,its convergence is proved by using the singular value decomposition,the orthogonal invariance of F-norm and the properties for solutions of the matrix equations and the estimation of its convergence rate is obtained;finally,numerical examples are given to verify the validity of the algorithm.

Key words: matrix equations, general solution, orthogonal projection iteration method, optimal approximation, minimum norm solution

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