Nonlinear eigenvalue problems and contour integrals

DOI10.1016/j.cam.2015.07.012zbMath1329.65109OpenAlexW1142570554MaRDI QIDQ495086

Peter Kravanja, Marc Van Barel

Publication date: 9 September 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.2015.07.012

zbMATH Keywords

nonlinear eigenvalue problemscontour integralsfilter functioncanonical polyadic decompositionBeyn's algorithmKeldysh' theorem

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Nonlinear spectral theory, nonlinear eigenvalue problems (47J10) Moment problems and interpolation problems in the complex plane (30E05) Numerical solution of nonlinear eigenvalue and eigenvector problems (65H17)

Related Items (15)

A Riesz-projection-based method for nonlinear eigenvalue problems ⋮ Beyond Automated Multilevel Substructuring: Domain Decomposition with Rational Filtering ⋮ Relationships among contour integral-based methods for solving generalized eigenvalue problems ⋮ Efficient resonance computations for Helmholtz problems based on a Dirichlet-to-Neumann map ⋮ Contour Integral Methods for Nonlinear Eigenvalue Problems: A Systems Theoretic Approach ⋮ Contour Integration for Eigenvector Nonlinearities ⋮ The nonlinear eigenvalue problem ⋮ Physically agnostic quasi normal mode expansion in time dispersive structures: from mechanical vibrations to nanophotonic resonances ⋮ Complex moment-based eigensolver coupled with two Krylov subspaces ⋮ Projection Method for Eigenvalue Problems of Linear Nonsquare Matrix Pencils ⋮ Computing Partial Spectra with Least-Squares Rational Filters ⋮ Computing resonant modes of accelerator cavities by solving nonlinear eigenvalue problems via rational approximation ⋮ A Rational QZ Method ⋮ A contour-integral based method with Schur-Rayleigh-Ritz procedure for generalized eigenvalue problems ⋮ An algorithm for identifying eigenvectors exhibiting strong spatial localization

Uses Software

• FEAST
• NLEVP
• CIRR
• Tensorlab

Cites Work

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• Tensor Decompositions and Applications
• An integral method for solving nonlinear eigenvalue problems
• A numerical method for polynomial eigenvalue problems using contour integral
• Contour integral eigensolver for non-Hermitian systems: a Rayleigh-Ritz-type approach
• A projection method for generalized eigenvalue problems using numerical integration.
• Dissecting the FEAST algorithm for generalized eigenproblems
• Computing the zeros of analytic functions
• CIRR: a Rayleigh-Ritz method with contour integral for generalized eigenvalue problems
• A filter diagonalization for generalized eigenvalue problems based on the Sakurai-Sugiura projection method
• A quadrature-based eigensolver with a Krylov subspace method for shifted linear systems for Hermitian eigenproblems in lattice QCD
• A numerical method for nonlinear eigenvalue problems using contour integrals
• FEAST As A Subspace Iteration Eigensolver Accelerated By Approximate Spectral Projection
• Numerical Algorithms Based on Analytic Function Values at Roots of Unity
• Zolotarev Quadrature Rules and Load Balancing for the FEAST Eigensolver
• A projection method for nonlinear eigenvalue problems using contour integrals
• Exponential data fitting using multilinear algebra: the single‐channel and multi‐channel case
• Computing $A^\alpha, \log(A)$, and Related Matrix Functions by Contour Integrals
• Computing Eigenvalues of Real Symmetric Matrices with Rational Filters in Real Arithmetic
• A Numerical Method for Locating the Zeros of an Analytic Function

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