Finite iterative algorithms for the reflexive and anti-reflexive solutions of the matrix equation A1X1B1+A2X2B2=C

Authors:
Mehdi Dehghan;Masoud Hajarian
Affiliations:
Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, No. 424, Hafez Avenue, Tehran 15914, Iran;Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, No. 424, Hafez Avenue, Tehran 15914, Iran
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2009

Citing 14
Cited 4

Topics in matrix analysis

Topics in matrix analysis
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Comments on "Finite iterative algorithms for the reflexive and anti-reflexive solutions of the matrix equation A 1X1B1+A2X2B2=C"

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Abstract

A matrix P@?R^n^x^n is called a generalized reflection matrix if P^T=P and P^2=I. An nxn matrix A is said to be a reflexive (anti-reflexive) matrix with respect to the generalized reflection matrix P if A=PAP(A=-PAP). In this paper, three iterative algorithms are proposed for solving the linear matrix equation A"1X"1B"1+A"2X"2B"2=C over reflexive (anti-reflexive) matrices X"1 and X"2. When this matrix equation is consistent over reflexive (anti-reflexive) matrices, for any reflexive (anti-reflexive) initial iterative matrices, the reflexive (anti-reflexive) solutions can be obtained within finite iterative steps in the absence of roundoff errors. By the proposed iterative algorithms, the least Frobenius norm reflexive (anti-reflexive) solutions can be derived when spacial initial reflexive (anti-reflexive) matrices are chosen. Furthermore, we also obtain the optimal approximation reflexive (anti-reflexive) solutions to the given reflexive (anti-reflexive) matrices in the solution set of the matrix equation. Finally, some numerical examples are presented to support the theoretical results of this paper.