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On Smooth LU Decompositions with Applications to Solutions of Nonlinear Eigenvalue Problems

On Smooth LU Decompositions with Applications to Solutions of Nonlinear Eigenvalue Problems
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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.

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