A Parallel Preconditioned Modified Conjugate Gradient Method for Large Sylvester Matrix Equation

Computational effort of solving large-scale Sylvester equations AX+XB+F=O is frequently hindered in dealing with many complex control problems. In this work, a parallel preconditioned algorithm for solving it is proposed based on combination of a parameter iterative preconditioned method and modifie...

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Veröffentlicht in:Mathematical problems in engineering 2014-01, Vol.2014 (2014), p.1-7
Hauptverfasser: Hou, Junxia, Lv, Quanyi, Xiao, Manyu
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Xiao, Manyu
description Computational effort of solving large-scale Sylvester equations AX+XB+F=O is frequently hindered in dealing with many complex control problems. In this work, a parallel preconditioned algorithm for solving it is proposed based on combination of a parameter iterative preconditioned method and modified form of conjugate gradient (MCG) method. Furthermore, Schur’s inequality and modified conjugate gradient method are employed to overcome the involved difficulties such as determination of parameter and calculation of inverse matrix. Several numerical results finally show that high performance of proposed parallel algorithm is obtained both in convergent rate and in parallel efficiency.
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subjects Algorithms
Computational efficiency
Computing time
Conjugate gradient method
Control theory
Efficiency
Inequalities
Inverse
Inverse matrices
Iterative methods
Mathematical analysis
Mathematical models
Matrix
Parameter modification
title A Parallel Preconditioned Modified Conjugate Gradient Method for Large Sylvester Matrix Equation
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