Numerical accuracy of converging sequences
Fabienne Jézéquel · HAL (Le Centre pour la Communication Scientifique Directe) · 2001
If we compute a sequence having a linear convergence until the difference between two successive iterates is not significant, the result obtained has the best numerical accuracy for the computer used. Furthermore its exact significant digits are those of the mathematical value of the limit, up to one bit. This strategy can be used for the trapezoidal or Simpson’s method, a sequence is then generated by halving the step value at each iteration. For Romberg’s method, which consists in computing a sequence having a super-linear convergence, a similar strategy can also be used.