| 预条件USSOR迭代法及比较定理 |
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| 引用本文： | 田秋菊,李金秋.预条件USSOR迭代法及比较定理[J].辽宁石油化工大学学报,2011,31(4):91-94. |
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| 作者姓名： | 田秋菊 李金秋 |
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| 作者单位： | 辽宁石油化工大学理学院,辽宁抚顺,113001 |
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| 摘 要： | 在预条件矩阵P=I+R下,提出了新的USSOR迭代法。通过矩阵理论,证明了在非奇异M-矩阵和非奇异H-矩阵下该预条件USSOR迭代法收敛,并给出了非奇异M-矩阵下预条件USSOR迭代法与经典USSOR迭代法的比较性定理,揭示了该预条件加快了USSOR迭代法的收敛速度,最后用数值例子验证了定理的正确性。
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| 关 键 词： | 预条件 USSOR迭代法 比较定理 |
Preconditioned USSOR Iterative Method and Comparison Theorem |
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| TIAN Qiu-ju,LI Jin-qiu.Preconditioned USSOR Iterative Method and Comparison Theorem[J].Journal of Liaoning University of Petroleum & Chemical Technology,2011,31(4):91-94. |
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| Authors: | TIAN Qiu-ju LI Jin-qiu |
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| Affiliation: | (College of Sciences,Liaoning Shihua University,Fushun Liaoning 113001,P.R.China) |
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| Abstract: | Under the preconditioned matrix P=I+R,the new USSOR iterative method was put forward.By the theory of matrix,it proved the convergence of the preconditioned USSOR iterative method when the coefficient matrix is a M-matrix or an H-matrix,gave a comparison theorem between the preconditioned USSOR iterative method and the classic USSOR iterative method when the coefficient matrix is a M-matrix,and disclosed precondition iterative method accelerates the convergence speed of the USSOR iterative method.Then a numerical example was used to demonstrate the validity. |
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| Keywords: | Precondition USSOR iterative method Comparison theorem |
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