On two-grid convergence estimates Export

@article{citeulike:3352053, abstract = {We derive a new representation for the exact convergence factor of classical two-level and two-grid preconditioners. Based on this result, we establish necessary and sufficient conditions for constructing the components of efficient algebraic multigrid (AMG) methods. The relation of the sharp estimate to the classical two-level hierarchical basis methods is discussed as well. Lastly, as an application, we give an optimal two-grid convergence proof of a purely algebraic lsquowindowrsquo-AMG method. Published in 2005 by John Wiley \& Sons, Ltd.}, address = {Lawrence Livermore National Laboratory, Center for Applied Scientific Computing, P.O. Box 808, L-561, Livermore, CA 94551, U.S.A.; Department of Mathematics, Center for Computational Mathematics and Applications, The Pennsylvania State University, University Park, PA 16802, U.S.A.}, author = {Falgout, Robert D. and Vassilevski, Panayot S. and Zikatanov, Ludmil T.}, citeulike-article-id = {3352053}, citeulike-linkout-0 = {http://dx.doi.org/10.1002/nla.437}, citeulike-linkout-1 = {http://www3.interscience.wiley.com/cgi-bin/abstract/110486156/ABSTRACT}, doi = {10.1002/nla.437}, journal = {Numerical Linear Algebra with Applications}, keywords = {algebraic, convergence, multi-grid, preconditioning, schur-komplement}, number = {5-6}, pages = {471--494}, posted-at = {2008-09-29 11:29:52}, priority = {4}, title = {On two-grid convergence estimates}, url = {http://dx.doi.org/10.1002/nla.437}, volume = {12}, year = {2005} }

TY - JOUR ID - citeulike:3352053 L3 - citeulike-article-id:3352053 N2 - We derive a new representation for the exact convergence factor of classical two-level and two-grid preconditioners. Based on this result, we establish necessary and sufficient conditions for constructing the components of efficient algebraic multigrid (AMG) methods. The relation of the sharp estimate to the classical two-level hierarchical basis methods is discussed as well. Lastly, as an application, we give an optimal two-grid convergence proof of a purely algebraic lsquowindowrsquo-AMG method. Published in 2005 by John Wiley & Sons, Ltd. IS - 5-6 JF - Numerical Linear Algebra with Applications AD - Lawrence Livermore National Laboratory, Center for Applied Scientific Computing, P.O. Box 808, L-561, Livermore, CA 94551, U.S.A.; Department of Mathematics, Center for Computational Mathematics and Applications, The Pennsylvania State University, University Park, PA 16802, U.S.A. EP - 494 TI - On two-grid convergence estimates VL - 12 SP - 471 KW - algebraic KW - convergence KW - multi-grid KW - preconditioning KW - schur-komplement AU - Falgout, Robert AU - Vassilevski, Panayot AU - Zikatanov, Ludmil PY - 2005/// UR - http://dx.doi.org/10.1002/nla.437 ER -