On the global Krylov subspace methods for solving general coupled matrix equations

Authors:
Fatemeh Panjeh Ali Beik;Davod Khojasteh Salkuyeh
Affiliations:
Department of Mathematics, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran;Department of Mathematics, University of Mohaghegh Ardabili, P.O. Box 179, Ardabil, Iran
Venue:
Computers & Mathematics with Applications
Year:
2011

Citing 7
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Abstract

In the present paper, we propose the global full orthogonalization method (Gl-FOM) and global generalized minimum residual (Gl-GMRES) method for solving large and sparse general coupled matrix equations @?j=1pA"i"jX"jB"i"j=C"i,i=1,...,p, where A"i"j@?R^m^x^m, B"i"j@?R^n^x^n, C"i@?R^m^x^n,i,j=1,2,...,p, are given matrices and X"i@?R^m^x^n, i=1,2,...,p, are the unknown matrices. To do so, first, a new inner product and its corresponding matrix norm are defined. Then, using a linear operator equation and new matrix product, we demonstrate how to employ Gl-FOM and Gl-GMRES algorithms for solving general coupled matrix equations. Finally, some numerical experiments are given to illustrate the validity and applicability of the results obtained in this work.