A Rayleigh quotient minimization algorithm based on algebraic multigrid | Zendy

Hetmaniuk U. | Zendy

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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

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.

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