线性互补问题基于模同步块二级多重分裂方法的收敛性分析  

Modulus-based Synchronous Block Two-stage Multisplitting Iteration Methods for Linear Complementarity Problems

作　　者：李燕[1] 汪祥[1] 毛良智[1] 

机构地区：[1]南昌大学数学系,江西南昌330031

出　　处：《南昌大学学报（工科版）》2013年第1期96-102,共7页Journal of Nanchang University(Engineering & Technology)

基　　金：国家自然科学基金资助项目(11101204);江西省青年科学家(井冈之星)资助项目(20122BCB23003);江西省自然科学基金资助项目(20114BAB201004);江西省教育厅科研资助项目(GJJ12011);江西省研究生创新资助项目(YC2011-S007;YC2012-S014)

摘　　要：研究了当系数矩阵的对角块为对称正定矩阵的块H矩阵时线性互补问题的数值求解。通过基于模分裂方法可将线性互补问题转化为只关于特殊向量模的不动点方程。结合块松驰迭代方法和基于模同步二级多重分裂迭代方法,将线性互补问题的系数矩阵是点的形式求解方法推广到块的形式,并且证明了新方法在满足适当条件下收敛。The linear complementarity problems have been considered is a block H matrix with the diagonal block symmetric positive definite. By in this paper, when the coefficient matrix splitting methods modulus-based, the linear complementarity problems can be transferred to fixed point systems of equations. Combining the block relaxed methods with modulus-based synchronous two-stage multi-splitting iteration methods, the generalized block form methods for solving the linear complementarity problems have been obtained. Moreover, we proved that the new methods will converge when some conditions are satisfied.

关 键 词：线性互补问题 块二级多重分裂 模方法 

分 类 号：O241.6[理学—计算数学]