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A wiggly function and its best approximations » Chebfun

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Ken Lord, whose doctoral supervisor was the Chebyshev technology wizard Charles Clenshaw, has explored functions of the form f(x)= T m (x)+ T m+1 (x)+⋯+ T n (x), 𝑓 ( 𝑥 ) = 𝑇 𝑚 ( 𝑥 ) + 𝑇 𝑚 + 1 ( 𝑥 ) + ⋯ + 𝑇 𝑛 ( 𝑥 ) , where T k 𝑇 𝑘 is the Chebyshev polynomial of degree k 𝑘 , as challenging functions for minimax approximation by polynomials of lower order. We can construct such functions in a single Chebfun command: For example, here we plot f(30,40) and its best approximation of degree 29 29 : Here are f(200,220) and its best approximation of degree 199 199 : © Copyright 2025 the University of Oxford and the Chebfun Developers.

Ken Lord, whose doctoral supervisor was the Chebyshev technology wizard Charles Clenshaw, has explored functions of the form $$ f(x) = T_m(x) + T_{m+1}(x) + \cdots + T_n(x), $$ where $T_k$ is the Chebyshev polynomial of degree $k$, as challenging functions for minimax approximation by polynomials of lower order. We can construct such functions in a single Chebfun command: fmn = @(m,n) sum(chebpoly(m:n),2); For example, here we plot f(30,40) and its best approximation of degree $29$: LW = 'linewidth'; FS = 'fontsize'; fs = 14; tic, m = 30; n = 40; f = fmn(m,n); subplot(2,2,1),…

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