Year: 2010
Journal of Computational Mathematics, Vol. 28 (2010), Iss. 6 : pp. 745–766
Abstract
We study the smooth LU decomposition of a given analytic functional $\lambda$-matrix $A(\lambda)$ and its block-analogue. Sufficient conditions for the existence of such matrix decompositions are given, some differentiability about certain elements arising from them are proved, and several explicit expressions for derivatives of the specified elements are provided. By using these smooth LU decompositions, we propose two numerical methods for computing multiple nonlinear eigenvalues of $A(\lambda)$, and establish their locally quadratic convergence properties. Several numerical examples are provided to show the feasibility and effectiveness of these new methods.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1004-m0009
Journal of Computational Mathematics, Vol. 28 (2010), Iss. 6 : pp. 745–766
Published online: 2010-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 22
Keywords: Matrix-valued function Smooth LU decomposition Pivoting Nonlinear eigenvalue problem Multiple eigenvalue Newton method.