This paper presents a modified HS conjugate gradient method for unconstrained optimization problem. The convergence of this algorithm is analyzed. Numerical experiments show that the algorithm is efficient by comparin...This paper presents a modified HS conjugate gradient method for unconstrained optimization problem. The convergence of this algorithm is analyzed. Numerical experiments show that the algorithm is efficient by comparing with HS conjugate gradient method under Armijo line search.展开更多
对大型稀疏的非Hermite正定线性代数方程组,运用正规和反Hermite分裂(normal and skew-Hermitian splitting,NSS)迭代技巧,提出了一种两参数预处理NSS迭代法,它实际上是预处理NSS方法的推广.理论分析表明,新方法收敛于线性方程组的唯一...对大型稀疏的非Hermite正定线性代数方程组,运用正规和反Hermite分裂(normal and skew-Hermitian splitting,NSS)迭代技巧,提出了一种两参数预处理NSS迭代法,它实际上是预处理NSS方法的推广.理论分析表明,新方法收敛于线性方程组的唯一解.进一步地,推导了出现于新方法中的两个参数的最优选取,计算了对应的迭代谱的上界的最小值.新方法的实际实施中,还将不完全LU分解和增量未知元选做了两类预处理子.数值结果对所给方法的收敛性理论和有效性予以了证实.展开更多
文摘This paper presents a modified HS conjugate gradient method for unconstrained optimization problem. The convergence of this algorithm is analyzed. Numerical experiments show that the algorithm is efficient by comparing with HS conjugate gradient method under Armijo line search.
基金Project supported by the National Basic Research Program of China(973 Program,2011CB706903)the Natural Science Foundation of Jilin Province of China(201115222)
文摘对大型稀疏的非Hermite正定线性代数方程组,运用正规和反Hermite分裂(normal and skew-Hermitian splitting,NSS)迭代技巧,提出了一种两参数预处理NSS迭代法,它实际上是预处理NSS方法的推广.理论分析表明,新方法收敛于线性方程组的唯一解.进一步地,推导了出现于新方法中的两个参数的最优选取,计算了对应的迭代谱的上界的最小值.新方法的实际实施中,还将不完全LU分解和增量未知元选做了两类预处理子.数值结果对所给方法的收敛性理论和有效性予以了证实.
