Convergence Orders of Iterative Methods for Nonlinear Eigenvalue Problems

DOI10.1007/978-3-642-30316-6_10zbMath1263.65049OpenAlexW180620840MaRDI QIDQ4915476

Gerhard Unger

Publication date: 10 April 2013

Published in: Advanced Finite Element Methods and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-642-30316-6_10

zbMATH Keywords

numerical experimentsiterative methodsnonlinear eigenvalue problemsconvergence orderpolynomial eigenvalue problemsholomorphic eigenvalue problemsaugmented Newton methodnonlinear generalized Rayleigh quotient iteration

Mathematics Subject Classification ID

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

Related Items

Implicit algorithms for eigenvector nonlinearities ⋮ Disguised and new quasi-Newton methods for nonlinear eigenvalue problems ⋮ Physically agnostic quasi normal mode expansion in time dispersive structures: from mechanical vibrations to nanophotonic resonances ⋮ A survey on variational characterizations for nonlinear eigenvalue problems ⋮ Nonlinearizing Two-parameter Eigenvalue Problems

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• An integral method for solving nonlinear eigenvalue problems
• Convergence factors of Newton methods for nonlinear eigenvalue problems
• Nonlinear Rayleigh functionals
• Analyzing the convergence factor of residual inverse iteration
• On the convergence of the Rayleigh quotient iteration for the computation of the characteristic roots and vectors. III: Generalized Rayleigh quotient and characteristic roots with linear elementary divisors. IV: Generalized Rayleigh quotient for nonlinear elementary divisors
• A generalized Rayleigh quotient iteration for lambda-matrices
• A block Newton method for nonlinear eigenvalue problems
• Rayleigh quotient algorithms for nonsymmetric matrix pencils
• Classes of linear operators. Vol. I
• Numerical methods for finding multiple eigenvalues of matrices depending on parameters
• Photonic band structure calculations using nonlinear eigenvalue techniques
• On the numerical solution of nonlinear eigenvalue problems
• The solution of characteristic value-vector problems by Newton's method
• A numerical method for nonlinear eigenvalue problems using contour integrals
• Convergence Analysis of a Galerkin Boundary Element Method for the Dirichlet Laplacian Eigenvalue Problem
• NLEVP
• Residual Inverse Iteration for the Nonlinear Eigenvalue Problem
• Inverse Iteration, Ill-Conditioned Equations and Newton’s Method
• Nonlinear eigenvalue problems: a challenge for modern eigenvalue methods
• On an Approach to the Solution of the Generalized Latent Value Problem for $\lambda $-Matrices
• AN OPERATOR GENERALIZATION OF THE LOGARITHMIC RESIDUE THEOREM AND THE THEOREM OF ROUCHÉ
• Algorithms for the Nonlinear Eigenvalue Problem
• Nichtlineare Behandlung von Eigenwertaufgaben
• A Survey of Open Cavity Scattering Problems