Contrôle dynamique de suites convergentes via l'Arithmétique Stochastique Discrète
Fabienne Jézéquel · 2003
On a computer, the optimal number of iterations of a converging se-quence can be determined dynamically using Discrete Stochastic Arith-metic. Computations are performed until the dierence between two suc-cessive iterates is not signicant. If the sequence converges at least lin-early, we can estimate the signicant 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 dierence between two successive iterates is a signicant value. The exact signicant 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 innite interval, can also be dynamically controlled.