一种求解鞍点问题的广义预条件对称-反对称分裂迭代法  

ON GENERALIZED PRECONDITIONED HERMITIAN AND SKEW-HERMITIAN SPLITTING METHODS FOR SADDLE POINT PROBLEMS

作　　者：潘春平[1] 王红玉[1,2] 

机构地区：[1]浙江工业职业技术学院人文社科部,浙江绍兴312000 [2]华东师范大学数学系,上海200062

出　　处：《数值计算与计算机应用》2011年第3期174-182,共9页Journal on Numerical Methods and Computer Applications

基　　金：浙江工业职业技术学院科技计划项目基金资助(KY2010109)

摘　　要：鞍点问题的来源和应用都很广泛,如计算流体力学,约束最优化,约束加权最小二乘问题等。寻求快速有效地求解这类问题的算法具有很重要的现实意义.在白中治,Golub和潘建瑜提出的预条件对称/反对称分裂迭代法(PHSS)的基础上,通过引入新的待定参数对原有迭代算法进行加速的思想,本文提出了一种解鞍点问题的具有两个待定参数的广义预条件对称/反对称分裂迭代法(GPHSS),并给出了该算法收敛性的条件.数值例子表明:通过最优参数值的选择,新算法比PHSS算法具有更快的收敛速度和更小的迭代次数,选择了最优参数值后,可以提高算法的收敛效率.The saddle point problems（SPP） 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 saddle point problems. Bai, Golub and Pan recently studied an Preconditioned Hermitian and skew-Hermitian splitting methods（PHSS）. By further accelerating it with another parameter,we present the generalized Preconditioned Hermitian and skew-Hermitian splitting methods（GPHSS）. Under some suitable conditions, we give the convergence results. Numerical results show that the new methods are very effective.

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]