Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



Analysis of two-grid methods: The nonnormal case

Author: Yvan Notay
Journal: Math. Comp. 89 (2020), 807-827
MSC (2010): Primary 65F08, 65F10, 65F50, 65N22
Published electronically: July 11, 2019
MathSciNet review: 4044451
Full-text PDF
View in AMS MathViewer New

Abstract | References | Similar Articles | Additional Information

Abstract: Core results about the algebraic analysis of two-grid methods are extended in relations bounding the field of values (or numerical range) of the iteration matrix. On this basis, bounds are obtained on its norm and numerical radius, leading to rigorous convergence estimates. Numerical illustrations show that the theoretical results deliver qualitatively good predictions, allowing one to anticipate success or failure of the two-grid method. They also indicate that the field of values and the associated numerical radius are much more reliable convergence indicators than the eigenvalue distribution and the associated spectral radius. On this basis, some discussion is developed about the role of local Fourier or local mode analysis for nonsymmetric problems.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC (2010): 65F08, 65F10, 65F50, 65N22

Retrieve articles in all journals with MSC (2010): 65F08, 65F10, 65F50, 65N22

Additional Information

Yvan Notay
Affiliation: Service de Métrologie Nucléaire, Université Libre de Bruxelles (C.P. 165/84), 50, Av. F.D. Roosevelt, B-1050 Brussels, Belgium

Keywords: Iterative methods, convergence analysis, linear systems, multigrid, two-grid, nonnormal matrices, AMG, preconditioning
Received by editor(s): April 3, 2018
Received by editor(s) in revised form: March 5, 2019, and April 12, 2019
Published electronically: July 11, 2019
Additional Notes: The author is Research Director of the Fonds de la Recherche Scientifique – FNRS
Article copyright: © Copyright 2019 American Mathematical Society