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On optimal step‐length gradient eigensolvers
Author(s) -
Neymeyr Klaus
Publication year - 2011
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201110364
Subject(s) - rayleigh quotient , preconditioner , mathematics , eigenvalues and eigenvectors , convergence (economics) , rayleigh quotient iteration , inverse , minification , inverse iteration , conjugate gradient method , gradient method , iterative method , mathematical optimization , geometry , physics , quantum mechanics , economics , economic growth
Gradient iterations for the minimization of the Rayleigh quotient are robust and (with a proper preconditioning) fast iterations to compute approximations of the smallest eigenvalue of a self‐adjoint elliptic partial differential operator. Up to now sharp convergence estimates were only known for the basic fixed‐step size preconditioned gradient iteration (also called preconditioned inverse iteration). Recently sharp convergence estimates have been proved for optimal step size (preconditioned) gradient iterations. These new estimates are compared with previous results. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)