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Mathematics of Computation

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

Author: Edgar A. Cohen
Journal: Math. Comp. 27 (1973), 817-827
MSC: Primary 41A10
MathSciNet review: 0330843
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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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Keywords: Function and first derivative, near minimax norms, polynomial approximation, orthogonal basis of polynomials, generalized Chebyshev polynomial expansions, position and velocity data, linear transformation, almost orthogonal set, recurrence relation, normalizing coefficient, best fit, integrals of Chebyshev polynomials, computer programs, Simpson rule, Fourier coefficients, function and derivative deviations, constraint built into norm, derivative deviations near endpoints, convex combination of two integrals, uniqueness of the approximant, error bounds and topological properties
Article copyright: © Copyright 1973 American Mathematical Society