Tschebychev Approximation to the Equation of Thermogravimetric Data

Abstract

THE use of approximate expressions rather than tabulations for non-elementary functions, such as the exponential integral, is often predicated on the simplicity of computation and the attainable accuracy. Since approximations receive quite wide usage, it is generally recognized that many expressions of varying degrees of complexity and precision are available. However, it is not so widely realized by workers not directly concerned with numerical analysis that techniques exist which may be used to obtain maximum accuracy from given functional forms by varying appropriate constants within the expressions. Procedures which best achieve the desired result require that the constants be selected such that the maximum deviation of the approximant from the exact function be minimized over the selected range of the independent variable. This is a statement of the Tschebychev criterion (for a brief introduction see ref. 1). It is the purpose of this communication to present a Tschebychev approximation to the function p(x), given by Doyle² as: which occurs in the equation of the thermogravimetric data plot.