ISSN:
1572-9265
Keywords:
errors bounds
;
conjugate gradient
;
65F50
Source:
Springer Online Journal Archives 1860-2000
Topics:
Computer Science
,
Mathematics
Notes:
Abstract In this paper we consider computing estimates of the norm of the error in the conjugate gradient (CG) algorithm. Formulas were given in a paper by Golub and Meurant (1997). Here, we first prove that these expressions are indeed upper and lower bounds for the A-norm of the error. Moreover, starting from these formulas, we investigate the computation of the l 2-norm of the error. Finally, we define an adaptive algorithm where the approximations of the extreme eigenvalues that are needed to obtain upper bounds are computed when running CG leading to an improvement of the upper bounds for the norm of the error. Numerical experiments show the effectiveness of this algorithm.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1019178811767
Permalink
