求解对角占有线性方程组的一种有效算法  

An Effective Algorithm For Diagonally Dominant Tridiagonal Linear Systems

作　　者：汪保[1] 方晓健[1] 

机构地区：[1]宁波工程学院,浙江宁波315211

出　　处：《宁波工程学院学报》2013年第4期43-47,共5页Journal of Ningbo University of Technology

摘　　要：针对线性方程组的求解,通过引入参数矩阵,提出一种求解线性方程组的迭代方法。为保证算法的收敛性,使迭代矩阵的无穷范数最小,确定参数矩阵的参数,得到求解线性方程组的迭代格式,证明了算法求解对角占优线性方程组是收敛的。数值结果表明了算法的有效性。An iterative method is proposed to solve the linear equations by introducing a parameter matrix. The parameters can be determined by minimizing the infinite norm of iterative matrix to make sure the convergence of algorithm solving linear systems~ It is prove that the convergence of algorithm when linear systems with diagonally dominant matrix is solved. The results of numerical example show that the method is feasible.

关 键 词：线性方程组 对角占优矩阵 有限差分 热传导方程 

分 类 号：O241.82[理学—计算数学]