10/16/2010, 03:43 AM

(10/15/2010, 11:28 PM)sheldonison Wrote:Gottfried Wrote:A plot of the differences (absolute difference between the evaluations of the two methods) shows two surprising *spikes*. Possibly there is a method- or an implementation-specific anomaly/bug?

I see no evidence of any jumps in any of the first 25 derivatives of sexp(z), centered at z=I, which corresponds to the observed jump at exp(Pi*I/2). I generated these derivatives via Cauchy/Fourier integral, using a sample circle of radius=0.1 about sexp(z=I).

- Sheldon

You're right.

It seems the implementation-artifact is in my routine for the polynomial interpolation.

The current version includes a separation of the height-parameter in the integer( hi = floor(real(h))) and the fractional & imaginary-part ( hf = h - hi) to have the fractional iteration only from a (comfortable) small interval of its parameter. At phi = pi/2 the real(h) changes sign and the floor-function steps. Because with the 32x32-matrices the k-fold-iterates of 1/k-height-stepwidth diverge from the 1-fold iteration of 1-height-stepwidt by about 1e-5 this introduces that error at this height-value. (Perhaps I should introduce some linear stretching for the polynomial method... at least for the comparision-graphs... <umpff>)

Gottfried

Gottfried Helms, Kassel