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AOR方法的最优因子及效果分析

鄂维南   

  1. 中国科学院计算中心
  • 出版日期:1984-03-14 发布日期:1984-03-14

鄂维南. AOR方法的最优因子及效果分析[J]. 计算数学, 1984, 6(3): 329-333.

THE OPTIMAL PARAMETERS OF AOR METHOD AND THEIR EFFECT

  1. E Wei-nan Computing Center, Academia Sinica
  • Online:1984-03-14 Published:1984-03-14
在[1]中提出了解线性代数方程组 A_x=b (1)的AOR方法: x~(m+1)=L_(α,ω)x~(m)+ω(I-αL)~(-1)b, (2 L_(α,ω)=(I-αL)~(-1)[(1-ω)I+(ω-α)L+ωU], (3)其中A=I-L-U,L,U分别为严格下、上三角矩阵。AOR方法主要用于求解椭圆型离散化方程组,故上面可设diag(A)=I。现记B=L+U。 当(2),(3)中两个参数取相同值时,AOR方法退化为相应参数的SOR方法。一个自然的问题是:能否在(2),(3)中选取适当的参数α,ω,使相应的AOR方法比最优参
We give in this paper a comparison of the convergence rates of the AOR (Ac-celerated Overrelaxation) method with the SOR method. For this purpose, the optimalparameters of the AOR method have been found. The results indicate that for discre-tized elliptic problems, the AOR method usually can not be more effective that the SORmethod Incidentally, we point out that a result in Math. Comp. Vol. 36 pp 183-188 iswrong
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