Multiple-Precision Evaluation of the Airy Ai Function with Reduced Cancellation

@article{Chevillard2013MultiplePrecisionEO,
  title={Multiple-Precision Evaluation of the Airy Ai Function with Reduced Cancellation},
  author={S. Chevillard and M. Mezzarobba},
  journal={2013 IEEE 21st Symposium on Computer Arithmetic},
  year={2013},
  pages={175-182}
}
  • S. Chevillard, M. Mezzarobba
  • Published 2013
  • Mathematics, Computer Science
  • 2013 IEEE 21st Symposium on Computer Arithmetic
  • The series expansion at the origin of the Airy function Ai(x) is alternating and hence problematic to evaluate for x > 0 due to cancellation. Based on a method recently proposed by Gawronski, Müller, and Rein hard, we exhibit two functions F and G, both with nonnegative Taylor expansions at the origin, such that Ai(x) = G(x)/F(x). The sums are now well-conditioned, but the Taylor coefficients of G turn out to obey an ill-conditioned three-term recurrence. We use the classical Miller algorithm… CONTINUE READING

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