LIP6 2003/012
- Reports
Contrôle dynamique de suites convergentes via l'Arithmétique Stochastique Discrète - F. Jézéquel
- 18 pages - 09/12/2003- document en - http://www.lip6.fr/lip6/reports/2003/lip6.2003.012.pdf - 255 Ko
- Contact :
- Ancien Thème : ANP
- Keywords : converging sequences, numerical validation, quadrature methods, trapezoidal method, Simpson's method, CESTAC method, Discrete Stochastic Arithmetic
- Publisher : Jean-Marie.Chesneaux (at) nulllip6.fr
On a computer, the optimal number of iterations of a converging sequence can be determined dynamically using Discrete Stochastic Arithmetic. Computations are performed until the difference between two successive iterates is not significant. If the sequence converges at least linearly, we can estimate the significant digits of the approximation common with the exact limit. This strategy can be used for the computation of integrals with the trapezoidal or Simpson's method. A sequence is then generated by halving the step value at each iteration, while the difference between two successive iterates is a significant value. The exact significant digits of the last iterate are those of the exact value of the integral, up to one bit. Numerical algorithms involving several sequences, such as the approximation of integrals on an infinite interval, can also be dynamically controlled.