A successive quadratic approximations method for nonlinear eigenvalue problems

DOI10.1016/j.cam.2015.05.011zbMath1321.65083OpenAlexW361443109MaRDI QIDQ492077

Xiaoyan Qian, Li Wang, Yong-Zhong Song

Publication date: 19 August 2015

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2015.05.011

zbMATH Keywords

convergencelinearizationeigenvectornonlinear eigenvalue problemnumerical experimentsuccessive quadratic approximations

Mathematics Subject Classification ID

Numerical solution of nonlinear eigenvalue and eigenvector problems (65H17)

Related Items

Eigenvibrations of a beam with elastically attached load, Eigenvibrations of a beam with load, Finite element approximation of the minimal eigenvalue of a nonlinear eigenvalue problem, Finite element approximation of the minimal eigenvalue and the corresponding positive eigenfunction of a nonlinear Sturm-Liouville problem, Error of the finite element approximation for a differential eigenvalue problem with nonlinear dependence on the spectral parameter, Approximation of positive semidefinite nonlinear eigenvalue problems

Cites Work

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• Recursive numerical recipes for the high efficient inversion of the confluent Vandermonde matrices
• A linear eigenvalue algorithm for the nonlinear eigenvalue problem
• Numerical recipes for the high efficient inverse of the confluent Vandermonde matrices
• Chebyshev interpolation for nonlinear eigenvalue problems
• Existence and location of eigenvalues for fluid-solid structures
• A block Newton method for nonlinear eigenvalue problems
• The rational Krylov algorithm for nonlinear matrix eigenvalue problems
• An Arnoldi method for nonlinear eigenvalue problems
• On the A-stable methods in the GBDF class
• Jacobi-Davidson type methods for generalized eigenproblems and polynomial eigenproblems
• Preconditioned iterative methods for a class of nonlinear eigenvalue problems
• The stability problem for linear multistep methods: old and new results
• An Arnoldi type projection method for nonlinear symmetric eigenproblems
• Derivatives of Eigenvalues and Eigenvectors of Matrix Functions
• Linearization of matrix polynomials expressed in polynomial bases
• Residual Inverse Iteration for the Nonlinear Eigenvalue Problem
• Numerical Solution of Quadratic Eigenvalue Problems with Structure-Preserving Methods
• Nonlinear eigenvalue problems: a challenge for modern eigenvalue methods
• Algorithms for the Nonlinear Eigenvalue Problem
• Computational Science - ICCS 2004