Rational Function Approximation of Polynomials to Give an Equiripple Error

A method is proposed whereby any polynomial can be approximated in an equiripple manner by a rational function. The properties and construction of such a rational function are discussed. Some of the advantages of the proposed form are: 1) approximations with less than the maximum number of ripples can be obtained, 2) the location of the error extrema within the approximation interval can be specified, and 3) polynomials more general than a constant can be approximated. Several examples are used to illustrate the theory.