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

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...

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Bibliographic Details
Published in:Computational mathematics and mathematical physics 2015-10, Vol.55 (10), p.1606-1618
Main Authors: Beik, Fatemeh Panjeh Ali, Salkuyeh, Davod Khojasteh
Format: Article
Language:English
Subjects:
Algorithms
Applied mathematics
Computation
Computational mathematics
Computational Mathematics and Numerical Analysis
Control theory
Convergence
Iterative methods
Joining
Linear equations
Links
Mathematical analysis
Mathematical models
Mathematics
Mathematics and Statistics
Methods
Studies
System theory
Topological manifolds
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Summary: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.
ISSN:0965-5425
1555-6662
DOI:10.1134/S0965542515100097