This article is cited in 8 papers

Weighted versions of Gl-FOM and Gl-GMRES for solving general coupled linear matrix equations

Fatemeh Panjeh Ali Beik^a, Davod Khojasteh Salkuyeh<sup>b

a</sup> Department of Mathematics, Vali-e-asr University of Rafsanjan, P. O. Box 518, Rafsanjan, Iran
^b Faculty of Mathematical Sciences, University of Guilan, P.O. Box 1914, Rasht, Iran

Abstract: In this paper, two algorithms called weighted Gl-FOM (WGl-FOM) and weighted Gl-GMRES (WGl-GMRES) are proposed for solving the general coupled linear matrix equations. In order to accelerate the speed of convergence, a new inner product is used. Invoking the new inner product and a new matrix product, the weighted global Arnoldi algorithm is introduced which will be utilized for employing the WGl-FOM and WGl-GMRES algorithms to solve the linear coupled linear matrix equations. After introducing the weighted methods, some relations that link Gl-FOM (Gl-GMRES) to its weighted version are established. Numerical experiments are presented to illustrate the effectiveness of the new algorithms in comparison with Gl-FOM and Gl-GMRES algorithms for solving the linear coupled linear matrix equations.

Key words: linear matrix equation, Krylov subspace, weighted methods, global FOM, global GMRES, global Arnoldi.

UDC: 519.612

Received: 15.11.2013

Language: English

DOI: 10.7868/S0044466915100099

 English version: Computational Mathematics and Mathematical Physics, 2015, 55:10, 1606–1618

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