A Preconditioned Iteration Method for Solving Sylvester Equations

A Preconditioned Iteration Method for Solving Sylvester Equations

A preconditioned gradient-based iterative method is derived by judicious selection of two auxil- iary matrices. The strategy is based on the Newton’s iteration method and can be regarded as ageneralization of the splitting iterative method for system of linear equations. We analyze the convergence o...

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Veröffentlicht in:Journal of Applied Mathematics 2012-01, Vol.2012 (2012), p.1183-1194-284
Hauptverfasser: Zhou, Jituan, Niu, Qiang, Wang, Ruirui
Format: Artikel
Sprache:eng
Schlagworte:
Algorithms
Convergence
Iterative methods
Linear equations
Mathematical analysis
Matrices
Matrix methods
Methods
Splitting
Strategy
Studies
System theory
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Zusammenfassung:A preconditioned gradient-based iterative method is derived by judicious selection of two auxil- iary matrices. The strategy is based on the Newton’s iteration method and can be regarded as ageneralization of the splitting iterative method for system of linear equations. We analyze the convergence of the method and illustrate that the approach is able to considerably accelerate the convergence of the gradient-based iterative method.
ISSN:1110-757X
1687-0042
DOI:10.1155/2012/401059