摘要
基于修正的埃尔米特和反埃尔米特分裂(MHSS)及预处理的MHSS(PMHSS)迭代法,提出了关于一类复对称线性方程组的单步MHSS(SMHSS)和单步PMHSS(SPMHSS)迭代法,进一步利用优化技巧给出了位移参数的动态选择格式,得出相应的带有灵活位移的SMHSS方法及SPMHSS迭代法.理论分析表明,迭代参数α在较弱的约束条件下,SMHSS迭代法收敛于复对称线性方程组的唯一解.同时,得到了SMHSS迭代矩阵的谱半径的上界,并且求得使上述上界最小的最优参数α~*.进一步给出了SPMHSS方法的收敛性分析.MHSS法和SMHSS迭代法之间的数值比较表明,在某些情况下,SMHSS迭代法比MHSS迭代法更优.
Based on the modified Hermitian and skew-Hermitian splitting （MHSS） and preconditioned MHSS （PMHSS） iteration methods, we present a single-step MHSS （SMHSS） and a single-step PMHSS （SPMHSS） iteration methods for a class of complex symmetric linear systems. The format of choosing a flexible shift- parameter is given by utilizing the optimization technique, and then we obtain the corresponding SMHSS and SPMHSS iteration methods with a flexible shift- parameter. Theoretical analysis shows that, under a weaker constraint condition on the iteration parameter , the SMHSS iteraton method is convergent to the unique solution of complex symmetric linear systems. Meanwhile, we derive an up- per bound for spectral radius of the SMHSS iteration matrix, and the quasi-optimal parameter is obtained by minimizing the above upper bound. Furthermore, theconvergence analysis of the SPMHSS iteration methods is given. Numerical ex- periments are reported to verify the efficiencies of several methods. Consequent comparisons show that the proposed SMHSS method is superior to the MHSS method under certain conditions.
出处
《应用数学与计算数学学报》
2017年第2期200-212,共13页
Communication on Applied Mathematics and Computation
基金
国家自然科学基金资助项目(11371275)
山西省自然科学基金资助项目(201601D011004)
关键词
复对称线性方程组
MHSS迭代法
收敛性
最优化
complex symmetric linear systems
modified Hermitian and skew-Hermitian splitting （MHSS） iteration method
convergence
optimization
