@Article{NMTMA-8-168,
author = {Yvan Notay},
title = {Algebraic Theory of Two-Grid Methods},
journal = {Numerical Mathematics: Theory, Methods and Applications},
year = {2015},
volume = {8},
number = {2},
pages = {168--198},
abstract = {<p style="text-align: justify;">About thirty years ago, Achi Brandt wrote a seminal paper providing a convergence theory for algebraic multigrid methods [Appl. Math. Comput., 19 (1986), pp. 23–56]. Since then, this theory has been improved and extended in a number of ways, and these results have been used in many works to analyze algebraic multigrid methods and guide their developments. This paper makes a concise exposition of the state of the art. Results for symmetric and nonsymmetric matrices are presented in a unified way, highlighting the influence of the smoothing scheme on the convergence estimates. Attention is also paid to sharp eigenvalue bounds for the case where one uses a single smoothing step, allowing straightforward application to deflation-based preconditioners and two-level domain decomposition methods. Some new results are introduced whenever needed to complete the picture, and the material is self-contained thanks to a collection of new proofs, often shorter than the original ones.</p>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.2015.w04si},
url = {http://global-sci.org/intro/article_detail/nmtma/12406.html}
}