A wiggly function and its best approximations » Chebfun

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.

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