05/24/2011, 02:22 PM
(05/23/2011, 08:42 PM)sheldonison Wrote: (...)Well, now I'm surprised. I've get that coefficients -however accurate only up to 6 digits, but maybe they converge if I use higher precision - by the most simple eigen-decomposition of the 32x32 carleman matrix.
Code:a0 = 0
a1 = 1.661129667441415
a2 = -1.137387400487982
a3 = 0.841151615164940
a4 = -0.657512962174043
a5 = 0.535494578310460
a6 = -0.449853109363909
a7 = 0.387026076215351
a8 = -0.339240627153272
a9 = 0.301798047541097
While the formal h'th powers of the carleman-matrices occur if I raise the diagonalmatrix of the eigenvalues to the h'th power, Pari/GP is able to convert this to a powerseries in x, if I enter the indeterminate x instead of a explicite h-value for the powers. (Note that this is the fourth method in my short treatize on "four methods of interpolation")
Well, Sheldon's method seem to allow much more precision and I do not see yet, how I could reproduce this by simply increasing the Pari/GP-resources in decimal precision and matrix-size.
Gottfried
Gottfried Helms, Kassel
