Marginal Utility in the Economization of Power Series

Abstract

This paper deals with a comparison of an ordinary power series in which the error tends to be large at the ends of the interval and small in the middle versus lower ordered Tschebyshev polynomials which result in minimum error at the ends of the interval. It is suggested that extrapolation error would be minimized through the use of Tschebyshev polynomials which converge more rapidly (have higher marginal utility per term) than any other set of orthogonal polynomials. It is further suggested that where possible a tradeoff be made of the marginal utility of adding another datum point to the sample versus adding another term to the power series, in order to achieve an “optimal” balance between these two contributors to error reduction.