Machine-efficient Chebyshev approximation for exact arithmetic: their use with first-order ordinary differential equations

TL;DR: It is demonstrated that these machine-efficient Chebyshev approximations do indeed improve the efficiency with which these operations can be performed.

Abstract: In this paper we use the idea of Brisebarre, Muller, Tisserand and Chevillard on machine-efficient Chebyshev approximation. Our aim is to provide high accuracy results for log, Gamma (and related functions), and the solution of Ordinary Differential Equations by Picard iteration using machine-efficient Chebyshev approximations. We demonstrate that these machine-efficient approximations do indeed improve the efficiency with which these operations can be performed. These practical calculations were performed using Muller's iRRAM.