On polynomial function approximation with minimum mean squared relative error and a problem of Tchebychef

Carlos F. Borges

Applied Mathematics and Computation, 2015, vol. 258, issue C, 22-28

Abstract: We consider the problem of constructing a polynomial approximation to a function f(x) over the interval [-1,1] that minimizes the mean squared relative error (MMSRE) over the interval. We establish sufficient conditions for solving the problem. We then consider a classic problem from a paper of Tchebychef and compare his solution to MMSRE, demonstrating that in some cases the latter approach can yield a more appealing solution and one that it is applicable in a number of situations where the Tchebychef approach is not.

Keywords: Approximation; Relative error; Least-squares (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:258:y:2015:i:c:p:22-28

DOI: 10.1016/j.amc.2015.01.121

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