File Exchange

image thumbnail

Fast Chebyshev transform

version 1.1 (1.42 KB) by

Fast computation of the Chebyshev transform



View License

fcht(V) computes the Chebyshev transform of a N+1 by 1 array V. If V corresponds to a function evaluated at the Chebyshev–Gauss–Lobatto points cos(pi*(0:N)/N), then V is interpolated by a linear combinations of the Chebyshev polynomials with weights given by fcht(V).
  Approximate f(x) = exp(x) over [-1,1] as a linear combination of the first three Chebyshev polynomials.
  x = cos(pi*(0:2)/2); % establish 3 Chebyshev grid points
  V = exp(x); % evaluate f(x) at Chebyshev grid points
  a = fcht(V);
  xx = linspace(-1,1); % create dense grid over domain
  g = a(1)*1 + a(2)*xx + a(3)*(2*xx.^2 - 1); % sum the first three Chebyshev
                % polynomials with respect to their corresponding weights
  plot(xx,exp(xx),xx,g); % visualize the approximation

Comments and Ratings (0)



matched usual naming convention

MATLAB Release
MATLAB 8.1 (R2013a)

Download apps, toolboxes, and other File Exchange content using Add-On Explorer in MATLAB.

» Watch video