• 0 Vote(s) - 0 Average
• 1
• 2
• 3
• 4
• 5
 Comparision: 4 different methods of interpolation Gottfried Ultimate Fellow Posts: 786 Threads: 121 Joined: Aug 2007 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... ) Gottfried Gottfried Helms, Kassel « Next Oldest | Next Newest »

 Messages In This Thread Comparision: 4 different methods of interpolation - by Gottfried - 10/13/2010, 01:32 AM RE: Comparision: 4 different methods of interpolation - by sheldonison - 10/14/2010, 11:14 PM RE: Comparision: 4 different methods of interpolation - by Gottfried - 10/15/2010, 02:07 PM RE: Comparision: 4 different methods of interpolation - by sheldonison - 10/15/2010, 03:07 PM RE: Comparision: 4 different methods of interpolation - by Gottfried - 10/15/2010, 04:14 PM RE: Comparision: 4 different methods of interpolation - by Gottfried - 10/15/2010, 04:41 PM RE: Comparision: 4 different methods of interpolation - by Gottfried - 10/15/2010, 09:19 PM RE: Comparision: 4 different methods of interpolation - by nuninho1980 - 10/15/2010, 04:18 PM RE: Comparision: 4 different methods of interpolation - by sheldonison - 10/15/2010, 11:28 PM RE: Comparision: 4 different methods of interpolation - by Gottfried - 10/16/2010, 03:43 AM

 Possibly Related Threads... Thread Author Replies Views Last Post On n-periodic points of the exp() - A discussion with pictures and methods Gottfried 1 2,099 06/10/2020, 09:34 AM Last Post: Gottfried

Users browsing this thread: 1 Guest(s)