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An accurate algorithm for evaluating rational functions

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  • Graillat, Stef

Abstract

Several different techniques intend to improve the accuracy of results computed in floating-point precision. Here, we focus on a method to improve the accuracy of the evaluation of rational functions. We present a compensated algorithm to evaluate rational functions. This algorithm is accurate and fast. The accuracy of the computed result is similar to the one given by the classical algorithm computed in twice the working precision and then rounded to the current working precision. This algorithm runs much more faster than existing implementation producing the same output accuracy.

Suggested Citation

  • Graillat, Stef, 2018. "An accurate algorithm for evaluating rational functions," Applied Mathematics and Computation, Elsevier, vol. 337(C), pages 494-503.
    • Handle: RePEc:eee:apmaco:v:337:y:2018:i:c:p:494-503
    DOI: 10.1016/j.amc.2018.05.039
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    References listed on IDEAS

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    1. Peibing Du & Hao Jiang & Lizhi Cheng, 2014. "Accurate Evaluation of Polynomials in Legendre Basis," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-13, July.
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    Cited by:

    1. Chuanying Li & Peibing Du & Kuan Li & Yu Liu & Hao Jiang & Zhe Quan, 2022. "Accurate Goertzel Algorithm: Error Analysis, Validations and Applications," Mathematics, MDPI, vol. 10(11), pages 1-19, May.

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