Nonlinear Rayleigh functionals

DOI10.1016/j.laa.2010.06.048zbMath1317.65100OpenAlexW2008065565MaRDI QIDQ414681

Hubert Schwetlick, Kathrin Schreiber

Publication date: 11 May 2012

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2010.06.048

zbMATH Keywords

Rayleigh quotientnonlinear eigenvalue problemperturbation of Rayleigh functionalsRayleigh functionalstationarity of Rayleigh functionals

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Spectrum, resolvent (47A10) Numerical solution of nonlinear eigenvalue and eigenvector problems (65H17)

Related Items (16)

Eigenvibrations of a beam with elastically attached load ⋮ A Block Preconditioned Harmonic Projection Method for Large-Scale Nonlinear Eigenvalue Problems ⋮ Eigenvibrations of a beam with load ⋮ The nonlinear eigenvalue problem ⋮ Local convergence analysis of several inexact Newton-type algorithms for general nonlinear eigenvalue problems ⋮ Rayleigh quotient minimization for absolutely one-homogeneous functionals ⋮ Finite element approximation of the minimal eigenvalue of a nonlinear eigenvalue problem ⋮ Modified successive approximation methods for the nonlinear eigenvalue problems ⋮ Convergence Orders of Iterative Methods for Nonlinear Eigenvalue Problems ⋮ Preconditioned eigensolvers for large-scale nonlinear Hermitian eigenproblems with variational characterizations. I. Extreme eigenvalues ⋮ Local convergence of Newton-like methods for degenerate eigenvalues of nonlinear eigenproblems. I. Classical algorithms ⋮ 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 ⋮ A survey on variational characterizations for nonlinear eigenvalue problems ⋮ What do you mean by ``Nonlinear eigenvalue problems? ⋮ Approximation of positive semidefinite nonlinear eigenvalue problems

Cites Work

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• A generalized Rayleigh quotient iteration for lambda-matrices
• A maxmin principle for nonlinear eigenvalue problems with application to a rational spectral problem in fluid-solid vibration.
• A block Rayleigh quotient iteration with local quadratic convergence
• An Arnoldi method for nonlinear eigenvalue problems
• The orthogonal Rayleigh quotient iteration (ORQI) method
• Two-sided and alternating Jacobi-Davidson
• Preconditioned iterative methods for a class of nonlinear eigenvalue problems
• Some variational principles for a nonlinear eigenvalue problem
• Variationsprinzipien bei nichtlinearen Eigenwertaufgaben
• Mehrparametrige und nichtlineare Eigenwertaufgaben
• A class of nonlinear eigenvalue problems
• Das Spektrum von Operatorscharen mit verallgemeinerten Rayleighquotienten
• A generalized Rayleigh quotient for eigenvalue problems nonlinear in the parameter
• A minimax theory for overdamped systems
• The Quadratic Eigenvalue Problem
• A minmax principle for nonlinear eigenproblems depending continuously on the eigenparameter
• Residual Inverse Iteration for the Nonlinear Eigenvalue Problem
• A minimax principle for nonlinear eigenvalue problems with applications to nonoverdamped systems
• The Rayleigh Quotient Iteration and Some Generalizations for Nonnormal Matrices
• Cubically Convergent Iterations for Invariant Subspace Computation
• A Jacobi–Davidson Iteration Method for Linear Eigenvalue Problems
• A Generalized Rayleigh Quotient Iteration for Computing Simple Eigenvalues of Nonnormal Matrices
• Eigenvalue Problems in Fiber Optic Design

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