On convergence of the modified Gauss-Seidel iterative method for \(H\)-matrix linear system (Q2851114)
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scientific article; zbMATH DE number 6214453
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On convergence of the modified Gauss-Seidel iterative method for \(H\)-matrix linear system |
scientific article; zbMATH DE number 6214453 |
Statements
9 October 2013
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modified Gauss-Seidel method
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preconditioner
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convergence
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\(H\)-matrix
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numerical experiment
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Toeplitz matrix
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On convergence of the modified Gauss-Seidel iterative method for \(H\)-matrix linear system (English)
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The authors propose a generalized pre-conditioner for a modified Gauss-Seidel method for solving a system of linear equations. They prove the convergence of the proposed method when the coefficient matrix is an \(H\)-matrix. Results of numerical experiments with different examples are given. These examples include Toeplitz matrices arising in many applications, such as solutions to differential and integral equations, spline functions, and problems and methods in physics, mathematics, statistics, and signal processing. The numerical results verify the given theoretical analysis.
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