高阶2PPJ迭代收敛的充要条件  

The necessary and sufficient condition of high order 2PPJ iteration convergence

作　　者：王晶 畅大为[1] 马静 WANG Jing;CHANG Dawei;MA Jing(School of Mathematics and Information Science,Shaanxi Normal University,Xi′an 710119,China)

机构地区：[1]陕西师范大学数学与信息科学学院

出　　处：《纺织高校基础科学学报》2019年第4期432-436,443,共6页Basic Sciences Journal of Textile Universities

基　　金：国家自然科学基金(11226266,11401361)

摘　　要：探讨线性方程组Ax=b的高阶2PPJ迭代收敛的充要条件。假设系数矩阵A的Jacobi矩阵特征值的平方为零或纯虚数,利用A的Jacobi矩阵特征值与高阶2PPJ迭代矩阵的关系,结合外插迭代引理,进一步给出此类方程组高阶2PPJ迭代收敛的充要条件。给出了2个数例对结论加以验证。The necessary and sufficient condition of high order 2PPJ iteration convergence of linear equations Ax=b was studied.First,assume the square of the eigenvalues of coefficient matrix A is zero or purely imaginary number,then the necessary and sufficient condition of high order 2PPJ iteration convergence of such linear equations can be obtanied by connecting the relations between the eigenvalue of Jacobi matrix of A and high order 2PPJ iteration matrix,as well as using the extrapolated iteration lemma.Finally,two numerical examples are proposed to verify the conclusions.

关 键 词：2PPJ迭代法 收敛性 特征值 外插迭代 JACOBI矩阵 

分 类 号：O241.6[理学—计算数学] TP301.1[理学—数学]