Application of homotopy perturbation methods for solving systems of linear equations |
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Authors: | Hsuan-Ku Liu |
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Institution: | Department of Mathematics and Information Education, National Taipei University of Education, Taiwan |
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Abstract: | In this paper, homotopy perturbation methods (HPMs) are applied to obtain the solution of linear systems, and conditions are deduced to check the convergence of the homotopy series. Moreover, we have adapted the Richardson method, the Jacobi method, and the Gauss-Seidel method to choose the splitting matrix. The numerical results indicate that the homotopy series converges much more rapidly than the direct methods for large sparse linear systems with a small spectrum radius. |
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Keywords: | HPM Linear systems Richardson method Jacobi method Gauss-Seidel method |
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