Frank Heckenbach frank@g-n-u.de a dit :
Besides, as I noted, Emil evaluates the series only in a certain interval (|u| < 1/3, i.e. z < 1/9), so the number of terms needed to get the required accuracy is bounded by a constant (the size of the coefficients array). When you say "too high", do you mean this constant is too big?
Bigger than that of a Tchebiceff polynomial of same accuracy over same range.
Also, as I said, I can't see why there should be large rounding errors.
Mmm. I may have spoken too fast. Rounding errors are a plague in large degree polynomials of alternating signs, if terms (coeff * x^n) are of same order of magnitude. This should not occur for an absolutely convergent series, where the higher degree terms are small, if summed from higher to lower degree.
Maurice
Maurice Lombardi wrote:
Also, as I said, I can't see why there should be large rounding errors.
Mmm. I may have spoken too fast. Rounding errors are a plague in large degree polynomials of alternating signs, if terms (coeff * x^n) are of same order of magnitude. This should not occur for an absolutely convergent series, where the higher degree terms are small, if summed from higher to lower degree.
That's what I meant (I forgot to mention this in my argumentation).
Frank