严格对角占优矩阵的SOR法收敛性和误差估计式

SOR-method Convergence and Error Estimate Formulain Strictly Diagonally Dominant Matrix

本文给出了严格对角占优矩阵 A 的 SOR 法(0<ω<c,c>1)收敛性和误差估计式,其误差估计常数 h_ω仅依赖于矩阵 A 的元素和松弛因子ω,从而避免了算 SOR 法迭代矩阵 L_ω=(D+ωL)^(-1)((1-ω)D-ωU)的麻烦,因此具有较好的实用价值.

This paper gives the SOR-method(0<ω<C,C>1)convergence and error estimate formula in strictly diagonally dominant matrix.The error esti- mate constant h_ω,depends only on the element of matrix A and the relaxation factor ω,and thus avoids trouble in computing SOR iterative matrix L_ω=(D+ ωL)^(-1)[(1-ω)D-ωU].Consequently,it has a fairly good practical value.