Polynomial approximation of a function and its first derivative in near minimax norms

Cohen, Edgar A.

doi:10.1090/S0025-5718-1973-0330843-6

Polynomial approximation of a function and its first derivative in near minimax norms
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Math. Comp. 27 (1973), 817-827 Request permission

Abstract:

Two near minimax norms for polynomial approximation are presented. They are designed for approximation of both a function and its first derivative uniformly by polynomials over a given finite interval. The first one is a convex combination of two integrals, one involving the function and the other the derivative, and the second is the sum of the square of the value of the function at one point and an integral involving the derivative. For any smooth function defined on a finite closed interval, one forms a generalized Chebyshev polynomial expansion to approximate both the function and derivative uniformly.

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Fourier Series