解具有周期边界条件的椭圆方程离散化线性方程组的PE_κ方法  

The PE_κ Method for Solving Linear Algebraic Equations Derived from Discretizing Elliptic Partial Differential Equation with Periodic Boundary Conditions

作　　者：周少玲[1] 张凯院[1] 

机构地区：[1]西北工业大学应用数学系,西安710072

出　　处：《工程数学学报》2005年第6期1013-1018,共6页Chinese Journal of Engineering Mathematics

基　　金：陕西省自然科学基金(2004CS110002).

摘　　要：建立了求解大型周期块状三对角线性代数方程组的PEκ方法。当线性方程组的系数矩阵为Hermite正定矩阵时,证明了PEκ方法的收敛性,并给出了参数k的选取范围。针对本文给出的算例,PE2方法的计算时间比SBGS方法节省50%。In this paper, we propose the PEk method for solving a system of large scale linear algebraic equations with periodic block-tridiagonal matrix. Under the condition that the coefficient matrix is Hermitian positive definite, the solvability and convergence of the new method are proved, and the selection range for the parameter k is given. For the example in this paper, the computation time of the PE2 method is only 50 percent of that of the SBGS method.

关 键 词：周期边界条件 椭圆型偏微分方程 周期块状三对角矩阵 PEk方法 

分 类 号：O241[理学—计算数学]