Designing rational filter functions for solving eigenvalue problems by contour integration

DOI10.1016/j.laa.2015.05.029zbMath1386.65115OpenAlexW624043996MaRDI QIDQ281986

Marc Van Barel

Publication date: 11 May 2016

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

Full work available at URL: https://doi.org/10.1016/j.laa.2015.05.029

zbMATH Keywords

resolventlinearnonlinear eigenvalue problemspolynomialrational approximationcontour integrationnonlinear least squaresfilter function

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane (30E20) Nonlinear spectral theory, nonlinear eigenvalue problems (47J10) Moment problems and interpolation problems in the complex plane (30E05)

Related Items (16)

A Riesz-projection-based method for nonlinear eigenvalue problems ⋮ Solving large‐scale nonlinear eigenvalue problems by rational interpolation and resolvent sampling based Rayleigh–Ritz method ⋮ Beyond Automated Multilevel Substructuring: Domain Decomposition with Rational Filtering ⋮ A Fast Contour-Integral Eigensolver for Non-Hermitian Matrices ⋮ Contour Integral Methods for Nonlinear Eigenvalue Problems: A Systems Theoretic Approach ⋮ The nonlinear eigenvalue problem ⋮ Solving large-scale interior eigenvalue problems to investigate the vibrational properties of the boson peak regime in amorphous materials ⋮ Fast Randomized Non-Hermitian Eigensolvers Based on Rational Filtering and Matrix Partitioning ⋮ Conversions between barycentric, RKFUN, and Newton representations of rational interpolants ⋮ Fast and backward stable computation of eigenvalues and eigenvectors of matrix polynomials ⋮ Computing Partial Spectra with Least-Squares Rational Filters ⋮ Computing resonant modes of accelerator cavities by solving nonlinear eigenvalue problems via rational approximation ⋮ A contour-integral based method with Schur-Rayleigh-Ritz procedure for generalized eigenvalue problems ⋮ Rational Spectral Filters with Optimal Convergence Rate ⋮ Coupled FE–BE method for eigenvalue analysis of elastic structures submerged in an infinite fluid domain ⋮ An algorithm for identifying eigenvectors exhibiting strong spatial localization

Uses Software

• FEAST
• NLEVP
• CIRR
• Tensorlab
• Complex Optimization Toolbox

Cites Work

• Tensor Decompositions and Applications
• An integral method for solving nonlinear eigenvalue problems
• A numerical method for polynomial eigenvalue problems using contour integral
• Reliably computing all characteristic roots of delay differential equations in a given right half plane using a spectral method
• Contour integral eigensolver for non-Hermitian systems: a Rayleigh-Ritz-type approach
• A projection method for generalized eigenvalue problems using numerical integration.
• A perturbation result for generalized eigenvalue problems and its application to error estimation in a quadrature method for computing zeros of analytic functions.
• An error analysis of two related quadrature methods for computing zeros of analytic functions.
• On locating clusters of zeros of analytic functions
• 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
• 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
• A Numerical Method for Locating the Zeros of an Analytic Function

This page was built for publication: Designing rational filter functions for solving eigenvalue problems by contour integration