polynomial_fit_chebyshev.jl

# polynomial n-degree Chebyshev fit example
# Juhani Kaukoranta 16.1.2024
using Plots,Polynomials,ApproxFun
n = 30; # pisteiden määrä
x = range(-1,1,length=n); # x n arvoa
f(x) = @. sqrt(1+x)*(sin(2*x)+cos(2*x)); # y n arvoa
cheby = Fun(f); # ApproxFun -> Chebyshev-sovitus
y = @. f(x); # original
p = fit(ChebyshevT, x, y, 5); map(x -> round(x, digits=6), p);
# p on Polynomials:n 5 degree Chebyshev-sovitus
scatter(x,y,title="Julian Chebyshev-sovituksia\n
f(x)=sqrt(x+1)*(sin(x)+cos(x))",label="original function")
plot!(x,cheby.(x),label="Chebyshev from Polynomials",lw=2)
plot!(x,p.(x),label ="Chebyshev 5 degr from ApproxFun",lw=2,ls=:dot)