Induced rational approximations of transcendental curves

Abstract

A novel technique for the construction of positive weight high-precision rational approximations to a class of transcendental curves is presented. The approximations are induced from the rational parametrisations of the circle. The previously published rational parametrisations of the circle are not suited to the induction process and the new parametrisations are constructed in the paper for the purpose. Explicit rational approximations of a number of transcendental curves are then given. The work is a development of the authors’ previous work on induced rational parametrisations of special algebraic curves.

Keywords:

• Rational approximation
• Transcendental curves
• Circle parametrisation
• Arc-length parametrisation
• Optimal parametrisation