Publisher review:Singular Fourier-Pade approximation - Circumvention of the Gibbs phenonmenon though Pade approximations with singularities Partial sums of Fourier terms for a function with jumps in value or derivative converge poorly, because of the Gibbs phenomenon. This file uses the Fourier coefficients, and locations of the singularities, to construct a different approximation that converges spectrally. For details, see T. A. Driscoll and B. Fornberg, Numerical Algorithms 26 (2001), pp. 77-92.Example for f(x)=|x|, using 7 Fourier coefficients:c = [pi/4 zeros(1,11)];c(2:2:12) = -(2/pi)*(1:2:11).^(-2);z0 = exp(1i*[-pi 0]);[p,q,r] = padelog(c,z0);Make a plot:x = linspace(-pi 10*eps,pi-10*eps,200); z = exp(1i*x);pz = polyval(p(end:-1:1),z);qz = polyval(q(end:-1:1),z);rz{1} = polyval(r{1}(end:-1:1),z);rz{2} = polyval(r{2}(end:-1:1),z);fplus = ( pz rz{1}.*log(1-z/z0(1)) rz{2}.*log(1-z/z0(2)) ) ./ qz;plot(x,abs(x),x,2*real(fplus),'k.') Requirements: ยท MATLAB Release: R14SP3
Singular Fourier-Pade approximation is a Matlab script for Mathematics scripts design by Tobin Driscoll.
It runs on following operating system: Windows / Linux / Mac OS / BSD / Solaris.
Operating system:Windows / Linux / Mac OS / BSD / Solaris
Singular Fourier-Pade approximation script details 
