An iterative algorithm for the least squares bisymmetric solutions of the matrix equations A1XB1=C1,A2XB2=C2

  • Authors:

  • Jing Cai;Guoliang Chen

  • Affiliations:

  • Department of Mathematics, East China Normal University, Shanghai 200062, People's Republic of China and School of Science, Huzhou Teachers College, Huzhou Zhejiang 313000, People's Republic of Ch ...;Department of Mathematics, East China Normal University, Shanghai 200062, People's Republic of China

  • Venue:
  • Mathematical and Computer Modelling: An International Journal
  • Year:
  • 2009

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Abstract

In this paper, an iterative algorithm is constructed to solve the minimum Frobenius norm residual problem: min@?(A"1XB"1A"2XB"2)-(C"1C"2)@? over bisymmetric matrices. By this algorithm, for any initial bisymmetric matrix X"0, a solution X^* can be obtained in finite iteration steps in the absence of roundoff errors, and the solution with least norm can be obtained by choosing a special kind of initial matrix. Furthermore, in the solution set of the above problem, the unique optimal approximation solution X@^ to a given matrix X@? in the Frobenius norm can be derived by finding the least norm bisymmetric solution of a new corresponding minimum Frobenius norm problem. Given numerical examples show that the iterative algorithm is quite effective in actual computation.