Interpolation - Fourier interpolant (i.e. trigonomentric) & Using Gauss-Legendre polynomial

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JaeSung Choi 2017-6-15

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https://ww2.mathworks.cn/matlabcentral/answers/344900-interpolation-fourier-interpolant-i-e-trigonomentric-using-gauss-legendre-polynomial

评论： Chaitral Date 2017-6-20

For example, f(x) = cos(x) in [-pi,pi]

1)I want to find Fourier(trigonomentric) interpolant. Is there any built in function for this interpolation? (such as 'interp1') If not, how can I do? Please give me some useful link or hint!

2)I want to find Gauss-Legendre polynomial of degree n(specified) My note says that if I use Gauss points and weights on the interval [1,1] I can find it. But actually i even don't know about Gauss points. (So I tried in wiki, but there wasn't) Same as 1) someone can give me some useful link or hint? Surely, built in function is nice if it exists.

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John D'Errico 2017-6-15

No, interp1 does not offer a Fourier interpolant.

You have it backwards on the Gauss-Legendre. You get nodes and weights from the polynomials.

There is a legendre function in MATLAB, that does return Legendre polynomials. Or I recall that my sympoly toolbox does have an orthpoly tool in it, that allows generation of polynomial families of all the standard types, in sympoly form.