摘要
在使用迭代法求解大型稀疏非奇异线性方程组时,引进由Chebyshev多项式形成的迭代向量{x(n)},对迭代过程进行加速,这是一种系统使用参数来加速的迭代法·在迭代向量序列{x(n)}形成的过程中,需要确定迭代参数序列{ρn}·对于斜对称化情况,迭代矩阵的特征值为纯虚数,且共轭成对地出现在虚轴上,而迭代参数序列{ρn}的确定恰取决于G迭代矩阵的谱半径S(G)的信息,即迭代参数序列{ρ2k}及{ρ2k+1}分别是单调增加和单调减少地收敛到同一个值,那么{ρn}必收敛且极限也是这个值,这样就可以利用极限值来选择一个最佳的迭代初值,从而使Chebyshev加速过程达到最优·
When the iterative method is used to solve the large, sparse and unsingular linear equations. Chebyshev polynomial can be introduced in the formation of the iterative vector {x^((n))} to accelerate the iterative process, i.e., an iterative method using systematically an acceleration parameter. In the formation process of the sequence of iterative vector {x_n}, the sequence of iterative parameter {ρ_n} is needed to decide. The eigenvalues of the iterative matrix are of the purely imaginary number under skew symmetrizable conditions and they appear conjugately in pairs along the imaginary axis, while the determination of the sequence of parameter {ρ_n} for skew-symmetrizable Chebyshev acceleration depends on the information on the spectrum S(G) of the iterative matrix G. It implies that the iterative parameter sets {ρ_(2k)} and {ρ_(2k+1)} are converged to the same value through monotone increasing and monotone decreasing, respectively. Then, {ρ_n} must be converged and limited to the same value. Thus, a limit value can be used to choose an optimal initial iterative value so as to optimize the process of Chebyshev acceleration.
出处
《东北大学学报（自然科学版）》
EI
CAS
CSCD
北大核心
2004年第1期96-98,共3页
Journal of Northeastern University(Natural Science)
基金
辽宁省自然科学基金资助项目(20022021).
