## Inverse fast Chebyshev transform

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Fast computation of the inverse Chebyshev transform

Updated 22 Oct 2013

ifcht(V) computes the inverse Chebyshev transform of a N+1 by 1 array A. If A corresponds to the weights of a linear combination of Chebyshev polynomials, then ifcht(a) computes the dataset interpolated by A at the Chebyshev–Gauss–Lobatto points cos(pi*(0:N)/N).

Example:
Suppose A = [3; 2; 1]. Then the function
f(x) = A(1)*1 + A(2)*x + A(3)*(2*x^2 - 1)
evaluated at x = cos(pi*(0:2)/2) = [1,0,-1] is given by ifcht(A).

x = cos(pi*(0:2)/2); %create Chebyshev grid of three points
xx = linspace(-1,1); % create dense grid over domain

A = [3; 2; 1];
f = A(1)*1 + A(2)*xx + A(3)*(2*xx.^2 - 1);

plot(xx,f,x,ifcht(A),'.','MarkerSize',20);

### Cite As

Matt (2023). Inverse fast Chebyshev transform (https://www.mathworks.com/matlabcentral/fileexchange/44033-inverse-fast-chebyshev-transform), MATLAB Central File Exchange. Retrieved .

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