Positive eigenvector of nonlinear eigenvalue problem with a singular M -matrix and Newton-SOR iterative solution

Journal of inequalities and applications

Cheng-yi Zhang¹ 

关键词: singular M-matrix;    nonlinear eigenvalue problem;    positive eigenvector;    Newton-SOR iterative solution;    convergence;    15A06;    15A15;    15A48;   

DOI  :  10.1186/s13660-016-1169-y

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

Some sufficient conditions are proposed in this paper such that the nonlinear eigenvalue problem with an irreducible singular M-matrix has a unique positive eigenvector. Under these conditions, the Newton-SOR iterative method is proposed for numerically solving such a positive eigenvector and some convergence results on this iterative method are established for the nonlinear eigenvalue problems with an irreducible singular M-matrix, a nonsingular M-matrix, and a general M-matrix, respectively. Finally, a numerical example is given to illustrate that the Newton-SOR iterative method is superior to the Newton iterative method.

【 授权许可】

CC BY