Recursive Krylov-based multigrid cycles

Numerical Linear Algebra with Applications

Volumn 15, Issue 5 SPEC. ISS., 2008, Pages 473-487

  Notay, Yvan ^a   Vassilevski, Panayot S ^b  

^a UNIVERSITÉ LIBRE DE BRUXELLES   (Belgium)

^b LAWRENCE LIVERMORE NATIONAL LABORATORY   (United States)

Author keywords

Conjugate gradients; Flexible conjugate gradients; Krylov subspace method; Multigrid; Preconditioning; Recursive multilevel Krylov iterations; Variable step multilevel preconditioning

Indexed keywords

EID: 51449112175     PISSN: 10705325     EISSN: None     Source Type: Journal    
DOI: 10.1002/nla.542     Document Type: Conference Paper

References (24)

1. Hackbusch W. Multi-grid Methods and Applications. Springer: Berlin, 1985.
2. Trottenberg U, Oosterlee CW, Schüller A. Multigrid. Academic Press: London, 2001.
3. Brandt A, McCormick SF, Ruge JW. Algebraic multigrid (AMG) for sparse matrix equations. In Sparsity and its Application, Evans DJ (ed.). Cambridge University Press: Cambridge, MA, 1984; 257-284.
4. Ruge JW, Stüben K. Efficient solution of finite difference and finite element equations by algebraic multigrid (AMG). In Multigrid Methods for Integral and Differential Equations, Paddon DJ, Holstein H (eds), The Institute of Mathematics and its Applications Conference Series. Clarendon Press: Oxford, 1985; 169-212.
5. Stuben K. An introduction to algebraic multigrid. In Multigrid, Trottenberg U, Oosterlee CW, Schüller A (eds). Academic Press: London, 2001; 413-532, Appendix A.
6. Brezina M, Cleary AJ, Falgout RD, Henson VE, Jones JE, Manteuffel TA, McCormick SF, Ruge JW. Algebraic multigrid based on element interpolation (AMGe). SIAM Journal on Scientific Computing 2000; 22:1570-1592.
7. Chattier T, Falgout RD, Henson VE, Jones J, Manteuffel T, McCormick S, Ruge J, Vassilevski PS. Spectral AMGe (pAMGe). SIAM Journal on Scientific Computing 2004; 25:1-26.
8. Cleary AJ, Falgout RD, Henson VE, Jones JE, Manteuffel TA, McCormick SF, Miranda GN, Ruge JW. Robustness and scalability of algebraic multigrid. SIAM Journal on Scientific Computing 2000; 21:1886-1908.
9. Saad Y. Iterative Methods for Sparse Linear Systems (2nd edn) SIAM: Philadelphia, PA, 2003.
10. van der Vorst HA. Iterative Krylov Methods for Large Linear Systems (2nd edn). Cambridge University Press: Cambridge, MA, 2003.
11. Axelsson O, Vassilevski PS. Variable-step multilevel preconditioning methods. I. Selfadjoint and positive definite elliptic problems. Numerical Linear Algebra with Applications 1994; 1:75-101.
12. Axelsson O, Vassilevski PS. A black-box generalized conjugate gradient solver with inner iterations and variable-step preconditioning. SIAM Journal on Matrix Analysis and Applications 1991; 12:625-644.
13. Saad Y. A flexible inner-outer preconditioned GMRES algorithm. SIAM Journal on Scientific Computing 1993; 14:461-469.
14. van der Vorst HA, Vuik C. GMRESR: a family of nested GMRES methods. Numerical Linear Algebra with Applications 1994; l(4):369-386.
15. Falgout RD, Vassilevski PS. On generalizing the algebraic multigrid framework. SIAM Journal on Numerical Analysis 2005; 42:1669-1693.
16. Notay Y. Algebraic multigrid and algebraic multilevel methods: a theoretical comparison. Numerical Linear Algebra with Applications 2005; 12:419-451.
17. Blaheta R. GPCG-generalized preconditioned CG method and its use with non-linear and non-symmetric displacement decomposition preconditioners. Numerical Linear Algebra with Applications 2002; 9:527-550.
18. Golub GH, Ye Q. Inexact preconditioned conjugate gradient method with inner-outer iterations. SIAM journal on Scientific Computing 1999; 21:1305-1320.
19. Notay Y. Flexible conjugate gradients. SIAM Journal on Scientific Computing 2000; 22:1444-1460.
20. Vassilevski PS. Multilevel Block Factorization Preconditioners. Springer: New York, 2007.
21. Falgout RD, Vassilevski PS, Zikatanov LT. On two-grid convergence estimates. Numerical Linear Algebra with Applications 2005; 12:471-494.
22. Kraus JK. An algebraic preconditioning method for M-matrices: linear versus nonlinear multilevel iteration. Numerical Linear Algebra with Applications 2002; 9:599-618.
23. Notay Y. Convergence analysis of perturbed two-grid and multigrid methods. SIAM Journal on Numerical Analysis 2007; 45:1035-1044.
24. Muresan AC, Notay Y. Analysis of aggregation-based multigrid. Technical Report GANMN 06-06, Université Libre de Bruxelles, Brussels, Belgium, 2006, http://homepages.ulb.ac.be/∼ynotay