On Polynomial Function Approximation with Minimum Mean Squared Relative Error and a Problem of Tchebychef
Borges, Carlos F.
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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.
The article of record as published may be found at: http://dx.doi.org/10.1016/j.amc.2015.01.121
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