High Accuracy Machine-Efficient Chebyshev Approximations: an Application to Spectral Methods for Sobolev Spaces

Mohammed Abutheraa, David Lester

Abstract

Machine-Efficient Chebyshev Approximation is a technique that permits practical evaluation of transcendental functions within a computable arithmetic, such as the computable reals. The approach adopts the usual Chebyshev method so that coefficients are efficiently handled by current computer hardware. The proposed technique has an application to spectral methods for sobolev spaces. A practical demonstration of this work is presented using M\"{u}ller's iRRAM exact arithmetic package. Experimental evaluation demonstrates that machine efficient approximations do indeed improve the efficiency with which these operations can be performed.

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