广义预条件对称-反对称分裂迭代法的收敛性分析  

On Convergence of Generalized Preconditioned Hermitian and Skew-Hermitian Splitting Methods

作　　者：潘春平[1] 

机构地区：[1]浙江工业职业技术学院人文社科部,绍兴312000

出　　处：《工程数学学报》2012年第5期733-740,共8页Chinese Journal of Engineering Mathematics

基　　金：浙江工业职业技术学院科技计划项目(1023401092012014)~~

摘　　要：为了高效地求解大型稀疏鞍点问题,在白中治等人提出的预条件对称–反对称分裂迭代法(PHSS)的基础上,本文通过引入新的待定参数对原有迭代算法进行加速的思想,提出了一种解鞍点问题的具有三个待定参数的广义预条件对称–反对称分裂迭代法(GPHSS),并在每一步迭代过程中采用直接法和内迭代相结合计算,给出了该算法收敛性的条件.理论上证明了算法的收敛性,数值算例表明算法是有效可行的.The saddle point problems arise from many areas of scientific research and engineering computations, such as computational fluid dynamics, constrained optimization and constrained and weighted least square problems. Therefore, it is of great interest to develop fast and efficient iterative methods for SPP. Bai et al recently studied an preconditioned Hermitian and skew-Hermitian split- ting methods （PHSS）. In this paper, we present the generalized PHSS methods with three parameter （GPHSS） by further accelerating it with another parameter, and we prove its convergence under suit- able restrictions on the iteration parameters. Numerical experiments show the presented algorithm is efficient.

关 键 词：鞍点问题 迭代法 HSS方法 PHSS方法 

分 类 号：O241.6[理学—计算数学]