4. Best polynomial approximation

Nevertheless, polynomials remain the simplest approximations for realizing the "fundamental idea". A natural approach is to give ourselves only degree n and try to find, for the function f ∊ C [a, b] under study, the polynomial of degree $\leq n$ that is closest to it. It can be shown that, for any $n \in ℕ$ , there exists a single polynomial $p_{n}^{*} \in Π_{n}$ ...

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Best polynomial approximation

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Interpolation between Chebyshev points

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Bibliography

(1) - BAKER (G.A.) Jr., GRAVES MORRIS (P.R.) - Padé Approximants, 2 ^nd ed - Cambridge University Press (1966).
(2) - BALTENSPERGER (R.) - Some results on linear rational trigonometric interpolation -...

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