Computational aspects of rational versus polynomial interpolations

Abstract

This article treats rational versus polynomial interpolative approximations as a subject for a mathematical laboratory. Rational interpolations are introduced in the guise of continued fractions. Using interpolative techniques, approximations with nearly equal ripple errors are constructed. The frequent superiority of rational over polynomial approximations is demonstrated by a number of representative examples. The choice of material, style and level of presentation were guided by pedagogical considerations. Emphasis is on the learning process in a mathematical laboratory environment.