High-Accuracy Machine-Efficient Chebyshev Approximation: An Application to Spectral methods for Sobolev spaces

Autores/as

  • Mohammed Abdulla Abutheraa The University of Manchester
  • David Lester The University of Manchester

DOI:

https://doi.org/10.1685/

Palabras clave:

(Chebyshev Polynomial, Computable Functions, Exact Real Arithmetic, Machine-Efficient Approximation, Partial Differential Equations)

Resumen

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 Müller's iRRAM exact arithmetic package. Experimental evaluation demonstrates that machine efficient approximations do indeed improve the efficiency with which these operations can be performed. [DOI: 10.1685/CSC09225] About DOI

Descargas

Publicado

2009-08-12

Número

Vol. 3 (2009)

Sección

Articles

Licencia

Authors who submit to this journal agree to the following terms: a) Authors retain copyright over their work, while allowing the SIMAI to place this accepted work under a Creative Commons Attribution License (CC license), which allows others to freely access, use, and share the work, with an acknowledgement of the work's authorship. b) Authors are able to waive the terms of the CC license and enter into separate, additional contractual arrangements for the non-exclusive distribution and subsequent publication of this work (e.g., publish a revised version in a journal, post it to an institutional repository or publish it in a book). with an acknowledgement of its initial publication on “Communications to SIMAI Congress”. c) In addition, authors are encouraged to post and share their work online (e.g., in institutional repositories or on their website).