Approximating monomials using Chebyshev polynomials

01/18/2021

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by   Arvind K. Saibaba, et al.

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This paper considers the approximation of a monomial x^n over the interval [-1,1] by a lower-degree polynomial. This polynomial approximation can be easily computed analytically and is obtained by truncating the analytical Chebyshev series expansion of x^n. The error in the polynomial approximation in the supremum norm has an exact expression with an interesting probabilistic interpretation. We use this interpretation along with concentration inequalities to develop a useful upper bound for the error.