Extreme eigenvalues of large sparse matrices by Rayleigh quotient and modified conjugate gradients

DOI10.1016/0045-7825(86)90041-1zbMath0579.65028OpenAlexW2032371871MaRDI QIDQ1067355

Giuseppe Gambolati, Anna Maria Perdon

Publication date: 1986

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0045-7825(86)90041-1

zbMATH Keywords

rate of convergencefinite elementRayleigh quotientCholesky factorizationconjugate gradientsextreme eigenvaluessymmetric positive-definite matrix

Mathematics Subject Classification ID

Computational methods for sparse matrices (65F50) Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Finite element methods applied to problems in solid mechanics (74S05) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30)

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CONJUGATE GRADIENT METHODS FOR SOLVING THE SMALLEST EIGENPAIR OF LARGE SYMMETRIC EIGENVALUE PROBLEMS ⋮ An improved iterative optimization technique for the leftmost eigenpairs of large symmetric matrices ⋮ Accelerated simultaneous iterations for large finite element eigenproblems ⋮ Computation of minimum eigenvalue through minimization of rayleigh's quotient for large sparse matrices using vector computer: ⋮ An orthogonal accelerated deflation technique for large symmetric eigenproblems ⋮ Computing several eigenpairs of Hermitian problems by conjugate gradient iterations ⋮ Multilevel preconditioned iterative eigensolvers for Maxwell eigenvalue problems ⋮ A method using successive iteration of analysis and design for large-scale topology optimization considering eigenfrequencies ⋮ 3-D nested eigenanalysis on finite element grids

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