The Advantages of Inverted Operators in Rayleigh–Ritz Approximations

DOI10.1137/0903006zbMath0477.65027OpenAlexW2051537564MaRDI QIDQ3935376

David S. Scott

Publication date: 1982

Published in: SIAM Journal on Scientific and Statistical Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/0903006

zbMATH Keywords

Lanczos algorithmsymmetric matricesRayleigh-Ritz proceduregeneralized eigenvalue problems

Mathematics Subject Classification ID

Numerical computation of eigenvalues and eigenvectors of matrices (65F15)

Related Items (16)

A generalized nonsymmetric Lanczos procedure ⋮ Numerical solution of large nonsymmetric eigenvalue problems ⋮ An invert-free Arnoldi method for computing interior eigenpairs of large matrices ⋮ Harmonic projection methods for large non-symmetric eigenvalue problems ⋮ Robust preconditioning of large, sparse, symmetric eigenvalue problems ⋮ A refined Arnoldi type method for large scale eigenvalue problems ⋮ Solving sparse symmetric definite quadratic lambda-matrix problems ⋮ Evaluation of matrix functions with the block Lanczos algorithm ⋮ The Lanczos algorithm for the generalized symmetric eigenproblem on shared-memory architectures ⋮ Generalizations of Davidson's method for computing eigenvalues of large nonsymmetric matrices ⋮ Fast eigenvalue calculations in a massively parallel plasma turbulence code ⋮ Rational Krylov sequence methods for eigenvalue computation ⋮ Filtering Frequencies in a Shift-and-Invert Lanczos Algorithm for the Dynamic Analysis of Structures ⋮ On the use of harmonic Ritz pairs in approximating internal eigenpairs ⋮ Computing interior eigenvalues of large matrices ⋮ A generalization of Saad's bound on harmonic Ritz vectors of Hermitian matrices

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