An improved iterative optimization technique for the leftmost eigenpairs of large symmetric matrices
type: Item
instance of: scholarly article
title: An improved iterative optimization technique for the leftmost eigenpairs of large symmetric matrices
zbMATH Open document ID: 0619.65027
DOI: 10.1016/0021-9991(88)90067-8
author: G. Gambolati
author: Giorgio Pini
author: Flavio Sartoretto
published in: Journal of Computational Physics
publication date: 1988-01-01T00:00:00Z
review text: An accelerated optimization technique combined with a stepwise deflation procedure is presented for the efficient evaluation of the p (p\(\leq 20)\) leftmost eigenvalues and eigenvectors of finite element symmetric positive definite matrices of very large size. The optimization is performed on the Rayleigh quotient of the deflated matrices by the aid of a conjugate gradient (CG) scheme effectively preconditioned with the incomplete Cholesky factorization. No ''a priori'' estimate of acceleration parameters is required. Numerical experiments on large arbitrarily sparse problems taken from the engineering finite elements practice show a very fast convergence rate for any value of p within the explored interval and particularly so for the minimal eigenpair. In this case the number of iterations needed to achieve an accurate solution may by as much as 2 orders of magnitude smaller than the problem size. Several results concerning the spectral behavior of the CG preconditioning matrices are also given and discussed.
Mathematics Subject Classification ID: 65F15
Mathematics Subject Classification ID: 65F35
Mathematics Subject Classification ID: 74S05
Mathematics Subject Classification ID: 65F50
zbMATH DE Number: 4005450
zbMATH Keywords: convergence acceleration
zbMATH Keywords: accelerated optimization technique
zbMATH Keywords: stepwise deflation procedure
zbMATH Keywords: leftmost eigenvalues
zbMATH Keywords: eigenvectors
zbMATH Keywords: finite element symmetric positive definite matrices
zbMATH Keywords: Rayleigh quotient
zbMATH Keywords: conjugate gradient scheme
zbMATH Keywords: incomplete Cholesky factorization
zbMATH Keywords: numerical experiments
zbMATH Keywords: very fast convergence rate
zbMATH Keywords: preconditioning matrices
MaRDI profile type: Publication
full work available at URL: 0021-9991(88)90067-8
OpenAlex ID: W2011000353
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description: scientific article; zbMATH DE number 4005450