Geometric interpretation of several classical iterative methods for linear system of equations and diverse relaxation parameter of the SOR method |
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Authors: | Xing-jiang Lu Lai-i Lei |
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Institution: | 1. Department of Mathematics, Zhejiang University, Hangzhou, 310027, China 2. Civil Engineering Laboratory of Macau, Macao, China
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Abstract: | Two kinds of iterative methods are designed to solve the linear system of equations, we obtain a new interpretation in terms of a geometric concept. Therefore, we have a better insight into the essence of the iterative methods and provide a reference for further study and design. Finally, a new iterative method is designed named as the diverse relaxation parameter of the SOR method which, in particular, demonstrates the geometric characteristics. Many examples prove that the method is quite effective. |
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Keywords: | linear equation iterative method geometric explanation diverse relaxation parameter SORmethod |
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