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On the convergence of two‐level Krylov methods for singular symmetric systems
Author(s) -
Erlangga Yogi A.,
Nabben Reinhard
Publication year - 2017
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.2108
Subject(s) - generalized minimal residual method , mathematics , convergence (economics) , residual , positive definite matrix , linear system , matrix (chemical analysis) , krylov subspace , iterative method , mathematical analysis , mathematical optimization , algorithm , eigenvalues and eigenvectors , physics , materials science , quantum mechanics , economics , composite material , economic growth
Summary We discuss the convergence of a two‐level version of the multilevel Krylov method for solving linear systems of equations with symmetric positive semidefinite matrix of coefficients. The analysis is based on the convergence result of Brown and Walker for the Generalized Minimal Residual method (GMRES), with the left‐ and right‐preconditioning implementation of the method. Numerical results based on diffusion problems are presented to show the convergence.