2010
DOI: 10.4208/jcm.1004-m0009
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On Smooth LU Decompositions with Applications to Solutions of Nonlinear Eigenvalue Problems

Abstract: We study the smooth LU decomposition of a given analytic functional λ-matrix A(λ) 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(λ), and establish their locally quadrat… Show more

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Cited by 16 publications
(1 citation statement)
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“…Both theoretical and numerical aspects of NEP were well investigated by the researchers. Various numerical methods such as classical Newton's method [30] block type Newton method [26], disguised and quasi-Newton method [20], LU-decomposition method [11], modified Newton's method [8], residual inverse iteration [29], Jacobi-Davidson type methods [4], implicit determinant method [37], method using contour integrals [1,3], Riesz-projected-based method [5], FEAST algorithm [14], Broyden's method [21] etc. were successfully applied for numerical solution of NEP.…”
Section: Nonlinearization Of 2pepmentioning
confidence: 99%
“…Both theoretical and numerical aspects of NEP were well investigated by the researchers. Various numerical methods such as classical Newton's method [30] block type Newton method [26], disguised and quasi-Newton method [20], LU-decomposition method [11], modified Newton's method [8], residual inverse iteration [29], Jacobi-Davidson type methods [4], implicit determinant method [37], method using contour integrals [1,3], Riesz-projected-based method [5], FEAST algorithm [14], Broyden's method [21] etc. were successfully applied for numerical solution of NEP.…”
Section: Nonlinearization Of 2pepmentioning
confidence: 99%