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A Rayleigh quotient minimization algorithm based on algebraic multigrid
Author(s) -
Hetmaniuk U.
Publication year - 2007
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/nla.545
Subject(s) - multigrid method , rayleigh quotient , mathematics , quotient , preconditioner , rayleigh quotient iteration , algebraic number , algorithm , minification , algebra over a field , mathematical optimization , pure mathematics , iterative method , mathematical analysis , partial differential equation , eigenvalues and eigenvectors , physics , quantum mechanics
Abstract This paper presents a new algebraic extension of the Rayleigh quotient multigrid (RQMG) minimization algorithm to compute the smallest eigenpairs of a symmetric positive definite pencil ( A , M ). Earlier versions of RQMG minimize the Rayleigh quotient over a hierarchy of geometric grids. We replace the geometric mesh information with the algebraic information defined by an algebraic multigrid preconditioner. At each level, we minimize the Rayleigh quotient with a block preconditioned algorithm. Numerical experiments illustrate the efficiency of this new algorithm to compute several eigenpairs. Copyright © 2007 John Wiley & Sons, Ltd.