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

Authors:
Mohammed A. Abutheraa;David Lester
Affiliations:
The University of Manchester, Manchester, United Kingdom;The University of Manchester, Manchester, United Kingdom
Venue:
SpringSim '10 Proceedings of the 2010 Spring Simulation Multiconference
Year:
2010

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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.