On two-grid convergence estimates

Numerical Linear Algebra with Applications

Volumn 12, Issue 5-6, 2005, Pages 471-494

  Falgout, Robert D ^a   Vassilevski, Panayot S ^a   Zikatanov, Ludmil T ^b  

^a LAWRENCE LIVERMORE NATIONAL LABORATORY   (United States)

^b PENNSYLVANIA STATE UNIVERSITY   (United States)

Author keywords

Algebraic multigrid; Convergence; Sharp estimates; Two grid; Two level methods

Indexed keywords

EID: 22144444957     PISSN: 10705325     EISSN: None     Source Type: Journal    
DOI: 10.1002/nla.437     Document Type: Article

References (16)

1. Axelsson O, Gustafsson I. Preconditioning and two-level multigrid methods of arbitrary degree of approximation. Mathematics of Computation 1983; 40:219-242.
2. Falgout RD, Vassilevski PS. On generalizing the AMG framework. SIAM Journal on Numerical Analysis 2004; 42:1669-1693.
3. Brandt A. General highly accurate algebraic coarsening. Electronic Transactions on Numerical Analysis 2000; 10:1-20.
4. Chartier T, Falgout R, Henson VE, Jones J, Manteuffel T, McCormick S, Ruge J, Vassilevski P. Spectral AMGe (pAMGe). SIAM Journal on Scientific Computing 2003; 25:1-26.
5. Bank RE, Dupont T. Analysis of a two-level scheme for solving finite element equations. Report CNA-159, Center for Numerical Analysis, The University of Texas at Austin, Austin, TX, 1980.
6. Braess D. The contraction number of a multigrid method for solving Poisson equation. Numerische Mathematik 1981; 37:387-404.
7. Yserentant H. On the multilevel splitting of finite element spaces. Numerische Mathematik 1986; 49:379-412.
8. Bank RE, Dupont T, Yserentant H. The hierarchical basis multigrid method. Numerische Mathematik 1988; 52:427-458.
9. Bank RE. Hierarchical Bases and the Finite Element Method. Acta Numerica, vol. 5. Cambridge University Press: Cambridge, 1996; 1-43.
10. Eijkhout VL, Vassilevski PS. The role of the C.B.S. inequality in multilevel methods. SIAM Review 1991; 33:405-419.
11. Vassilevski PS. On two ways of stabilizing the HB multilevel methods. SIAM Review 1997; 39:18-53.
12. Xu J, Zikatanov LT. The method of alternating projections and the method of subspace corrections in Hubert space. Journal of the American Mathematical Society 2002; 15:573-597.
13. Axelsson O. Iterative Solution Methods. Cambridge University Press: Cambridge, 1994.
14. Demko S, Moss WF, Smith PW. Decay rates of inverses of band matrices. Mathematics of Computation 1984; 43:491-499.
15. Ruge JW, Stüben K. Algebraic multigrid (AMG). In Multigrid Methods, McCormick SF (ed.). Frontiers in Applied Mathematics, vol. 3. SIAM: Philadelphia, PA, 1987; 73-130.
16. Briggs WL, Henson VE, McCormick SF. A Multigrid Tutorial (2nd edn). SIAM: Philadelphia, PA, 2000.