预条件USSOR迭代法及比较定理

doi:10.3696/j.issn.1672-6952.2011.03.024

辽宁石油化工大学学报 ›› 2011, Vol. 31 ›› Issue (4): 91-94.DOI: 10.3696/j.issn.1672-6952.2011.03.024

• 数学与管理 • 上一篇

预条件USSOR迭代法及比较定理

田秋菊，李金秋

辽宁石油化工大学理学院, 辽宁抚顺 113001

收稿日期:2011-02-15 出版日期:2011-12-25 发布日期:2017-07-14

Preconditioned USSOR Iterative Method and Comparison Theorem

TIAN Qiu-ju, LI Jin-qiu

College of Sciences, Liaoning Shihua University, Fushun Liaoning 113001, P.R.China

Received:2011-02-15 Published:2011-12-25 Online:2017-07-14

摘要/Abstract

摘要： 在预条件矩阵[WTHX]P=I+R[WTBZ]下,提出了新的USSOR迭代法。通过矩阵理论,证明了在非奇异[WTHX]M-矩阵和非奇异H-矩阵下该预条件[WTBZ]USSOR迭代法收敛，并给出了非奇异[WTHX]M-矩阵下预条件[WTBZ]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。

关键词: 预条件, USSOR迭代法, 比较定理

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.

Key words: Precondition, USSOR iterative method, Comparison theorem

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.

TIAN Qiu-ju, LI Jin-qiu. Preconditioned USSOR Iterative Method and Comparison Theorem[J]. Journal of Liaoning Petrochemical University, 2011, 31(4): 91-94.

预条件USSOR迭代法及比较定理

Preconditioned USSOR Iterative Method and Comparison Theorem

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