Geodesic
Weighted versions of Gl-FOM and Gl-GMRES for solving general coupled linear matrix equations
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 10, pp. 1606-1618

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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. 
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     author = {Fatemeh Panjeh Ali Beik and Davod Khojasteh Salkuyeh},
     title = {Weighted versions of {Gl-FOM} and {Gl-GMRES} for solving general coupled linear matrix equations},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1606--1618},
     publisher = {mathdoc},
     volume = {55},
     number = {10},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_10_a2/}
}
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Fatemeh Panjeh Ali Beik; Davod Khojasteh Salkuyeh. Weighted versions of Gl-FOM and Gl-GMRES for solving general coupled linear matrix equations. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 55 (2015) no. 10, pp. 1606-1618. http://geodesic.mathdoc.fr/item/ZVMMF_2015_55_10_a2/