摘要
本文利用Evans提出的PSD迭代方法来解决鞍点问题.该论文首先建立了PSD方法的迭代矩阵Sτ,ω,α的特征值λ和矩阵J=Q-1 BT A-1B的特征值μ之间所满足的基本关系式,然后讨论了PSD方法收敛的必要条件,最后着重讨论了ω=1时,PSD方法收敛的充分必要条件,并在合理的假设下得到了PSD方法收敛的最优参数和最优谱半径.
This paper solves the problem of large scale sparse saddle point with the PSD iterative method proposed by Evans.Firstly,the function equation among the eigenvalues of the iteration matrix of the PSD method and the matrix Q ？1 BT A？1B is established.Secondly,it discusses the necessary conditions for the convergence of the PSD method.Thirdly,the necessary and sufficient conditions for the convergence of the PSD method are derived by giving the restrictions imposed on the parameters,such as ω =1.Lastly,the optimum parameter and the most superior spectrum radius are obtained under certain conditions.
出处
《西南民族大学学报（自然科学版）》
CAS
2010年第3期387-391,共5页
Journal of Southwest Minzu University(Natural Science Edition)
基金
国家自然科学基金资助项目(60671063)
关键词
PSD迭代法
鞍点问题
最优参数
最优谱半径
PSD iterative solution
large scale sparse saddle point
optimum parameter
superior spectrum radius
