Differential equations and solution of linear systems

Numerical Algorithms

Volumn 40, Issue 2, 2005, Pages 103-124

  Chehab, Jean Paul ^a,b   Laminie, Jacques ^b  

^a UNIV LILLE   (France)

^b UNIVERSITÉ PARIS SUD   (France)

Author keywords

Differential equation; Numerical linear algebra; Numerical schemes; Preconditioning

Indexed keywords

EID: 27844572414     PISSN: 10171398     EISSN: 15729265     Source Type: Journal    
DOI: 10.1007/s11075-005-1523-5     Document Type: Conference Paper

References (20)

1. F. Alvarez, H. Attouch, J. Bolte and P. Redont, A second-order gradient-like dissipative dynamical system with Hessian-driven damping. Application to optimization and mechanics, J. Math. Pures Appl. 81 (2002) 747-779.
2. J. Barzilai and J.M. Borwein, Two points step size gradient methods, IMA J. Numer. Anal. 8 (1988) 141-148.
3. M. Benzi, Preconditioning techniques for large linear systems: A survey, J. Comput. Phys. 182 (2002) 418-477.
4. A. Bhaya and E. Kaszkurewicz, Iterative methods as dynamical systems with feedback control, Preprint, UFRJ, Department of Electrical Engineering (2003).
5. C. Brezinski, Variations on Richardson's method and acceleration, in: Numerical Analysis. A Numerical Analysis Conference in Honour of Jean Meinguet, Bull. Soc. Math. Belg. (1996) pp. 33-44.
6. C. Brezinski, Projection Methods for Systems of Equations (North-Holland, Amsterdam, 1997).
7. C. Brezinski, Difference and differential equations, and convergence acceleration algorithms, in: SIDE III - Symmetries and Integrability of Difference Equations, eds. D. Levi and O. Ragnisco, CRM Proceedings and Lecture Notes, Vol. 25 (AMS, Providence, RI, 2000).
8. C. Brezinski, Dynamical systems and sequence transformations, J. Phys. A: Math. Gen. 34 (2001) 10659-10669.
9. C. Brezinski and J.-P. Chehab, Nonlinear Hybrid Procedures and fixed point iterations, Numer. Funct. Anal. Optim. 19 (1998) 465-487.
10. J.-P. Chehab, Differential equations and inverse preconditioners, Prépublications d'Orsay 2002-20, submitted.
11. A. Cuyt and L. Wuytack, Nonlinear Methods in Numerical Analysis (North-Holland, Amsterdam, 1987).
12. R.W. Freund and N.M. Nachtigal, QMR a quasi-minimal residual method for non-Hermitian linear systems, Numer. Math. 60 (1991) 315-339.
13. U. Helmke and J.B. Moore, Optimization and Dynamical Systems (Springer, Berlin, 1994).
14. M.W. Hirsch and S. Smale, Differential Equations, Dynamical Systems and Linear Algebra (Academic Press, London, 1974).
15. J.H. Hubbard and B.H. West, Differential Equations. A Dynamical Systems Approach. Part I: Ordinary Differential Equations (Springer, New York, 1991).
16. F. Luengo, M. Raydan, W. Glunt and T.L. Hayden, Preconditioned spectral gradient method, Numer. Algorithms 30 (2002) 241-258.
17. J.M. Ortega and W.C. Rheinboldt, Iterative Solution of Nonlinear Equations in Several Variables (Academic Press, San Diego, 1970).
18. Y. Saad, Iterative Methods for Sparse Linear Systems (SIAM, Philadelphia, PA, 1996).
19. A.M. Stuart, Numerical analysis of dynamical systems, in: Acta Numerica (Cambridge Univ. Press, Cambridge, 1994) pp. 467-572.
20. H.A. Van der Vorst, Bi-Cgstab: A fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems, SIAM J. Sci. Statist. Comput. 13 (1992) 631-644.