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

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...

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Bibliographic Details
Published in:Journal of inequalities and applications Vol. 2016; no. 1; pp. 1 - 10
Main Authors: Zhang, Cheng-yi, Song, Yao-yan, Luo, Shuanghua
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 15.09.2016
Springer Nature B.V
SpringerOpen
Subjects:
Analysis
Applications of Mathematics
Convergence
Eigenvalues
Eigenvectors
Inequalities
Iterative methods
Iterative solution
Mathematical models
Mathematics
Mathematics and Statistics
Newton-SOR iterative solution
nonlinear eigenvalue problem
Nonlinearity
positive eigenvector
Recent Advances in Eigenvalues Estimates of Special Matrices (Tensors)
singular M-matrix
positive eigenvector
Newton-SOR iterative solution
convergence
15A06
15A15
15A48
singular
matrix
nonlinear eigenvalue problem
ISSN:1029-242X, 1025-5834, 1029-242X
Online Access:Get full text
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Summary: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.
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ISSN:1029-242X
1025-5834
1029-242X
DOI:10.1186/s13660-016-1169-y