Estimates of the l 2 norm of the error in the conjugate gradient algorithm

Numerical Algorithms

Volumn 40, Issue 2, 2005, Pages 157-169

  Meurant, Gérard ^a  

^a CEA DIF   (France)

Author keywords

Conjugate gradient; Norm of the error

Indexed keywords

EID: 27844568488     PISSN: 10171398     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11075-005-1528-0     Document Type: Conference Paper

References (11)

1. Z. Bai and G.H. Golub, Bounds for the trace of the inverse and the determinant of symmetric positive definite matrices, Ann. Numer. Math. 4 (1997) 29-38.
2. M. Benzi, C.D. Meyer and M. Tuma, A sparse approximate inverse preconditioner for the conjugate gradient method, SIAM J. Sci. Comput. 17 (1996) 1135-1149.
3. B. Fischer and G.H. Golub, On the error computation for polynomial based iteration methods, Report NA 92-21, Stanford University (1992).
4. B. Fischer, Polynomial Based Iteration Methods for Symmetric Linear Systems (Wiley/Teubner, New York/Stuttgard, 1996).
5. G.H. Golub and G. Meurant, Matrices, moments and quadrature, in: Numerical Analysis 1993, eds. D.F. Griffiths and G.A. Watson, Pitman Research Notes in Mathematics Series, Vol. 303 (Longman Sci. Tech., Harlow, 1994) pp. 105-156.
6. G.H. Golub and G. Meurant, Matrices, moments and quadrature II or how to compute the norm of the error in iterative methods BIT 37(3) (1997) 687-705.
7. G.H. Golub and Z. Strakǒs, Estimates in quadratic formulas, Numer. Algorithms 8(2-4) (1994).
8. G. Meurant, The computation of bounds for the norm of the error in the conjugate gradient algorithm, Numer. Algorithms 16 (1997) 77-87.
9. G. Meurant, Numerical experiments in computing bounds for the norm of the error in the preconditioned conjugate gradient algorithm, Numer. Algorithms 22 (1999) 353-365.
10. G. Meurant, Computer Solution of Large Linear Systems (North-Holland, Amsterdam, 1999).
11. Z. Strakǒs and P. Tichy, On error estimates in the conjugate gradient method and why it works in finite precision computations, ETNA 13 (2002) 56-80.