Adaptive eigenvalue computation: Complexity estimates

DOI10.1007/s00211-008-0159-5zbMath1157.65029arXiv0711.1070OpenAlexW2055232172MaRDI QIDQ958152

Wolfgang Dahmen, Reinhold Schneider, Thorsten Rohwedder, Andreas Zeiser

Publication date: 2 December 2008

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0711.1070

zbMATH Keywords

finite elementsHilbert spacepreconditioningfinite differencesRayleigh quotientSchrödinger equationadaptive algorithmcomplexity estimatessteepest descent methodstrongly positive operatoradaptive eigenvalue solveralgorithm MINIEIGalgorithm MINITeigenvalue problem in abstract spacelinear symmetric,bounded

Mathematics Subject Classification ID

Multigrid methods; domain decomposition for boundary value problems involving PDEs (65N55) Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Spectrum, resolvent (47A10) PDEs in connection with quantum mechanics (35Q40) Numerical solutions to equations with linear operators (65J10) Finite difference methods for boundary value problems involving PDEs (65N06) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25)

Related Items (9)

An adaptive algorithm based on the shifted inverse iteration for the Steklov eigenvalue problem ⋮ Adaptive computation of smallest eigenvalues of self-adjoint elliptic partial differential equations ⋮ The Shifted-Inverse Iteration Based on the Multigrid Discretizations for Eigenvalue Problems ⋮ Guaranteed lower bounds for eigenvalues ⋮ Perturbed preconditioned inverse iteration for operator eigenvalue problems with applications to adaptive wavelet discretization ⋮ An adaptive nonconforming finite element algorithm for Laplace eigenvalue problem ⋮ Finite element approximations of nonlinear eigenvalue problems in quantum physics ⋮ Adaptive wavelet methods for elliptic partial differential equations with random operators ⋮ Smoothed-adaptive perturbed inverse iteration for elliptic eigenvalue problems

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