About the Project
NIST

improved accuracy via numerical transformations

AdvancedHelp

(0.002 seconds)

3 matching pages

1: 2.11 Remainder Terms; Stokes Phenomenon
§2.11(vi) Direct Numerical Transformations
For example, extrapolated values may converge to an accurate value on one side of a Stokes line (§2.11(iv)), and converge to a quite inaccurate value on the other.
2: 9.17 Methods of Computation
Since these expansions diverge, the accuracy they yield is limited by the magnitude of | z | . However, in the case of Ai ( z ) and Bi ( z ) this accuracy can be increased considerably by use of the exponentially-improved forms of expansion supplied in §9.7(v). … A comprehensive and powerful approach is to integrate the defining differential equation (9.2.1) by direct numerical methods. …
§9.17(iv) Via Bessel Functions
Zeros of the Airy functions, and their derivatives, can be computed to high precision via Newton’s rule (§3.8(ii)) or Halley’s rule (§3.8(v)), using values supplied by the asymptotic expansions of §9.9(iv) as initial approximations. …
3: Bibliography N
  • M. Nardin, W. F. Perger, and A. Bhalla (1992a) Algorithm 707: CONHYP: A numerical evaluator of the confluent hypergeometric function for complex arguments of large magnitudes. ACM Trans. Math. Software 18 (3), pp. 345–349.
  • M. Nardin, W. F. Perger, and A. Bhalla (1992b) Numerical evaluation of the confluent hypergeometric function for complex arguments of large magnitudes. J. Comput. Appl. Math. 39 (2), pp. 193–200.
  • G. Nemes (2013b) Error bounds and exponential improvement for Hermite’s asymptotic expansion for the gamma function. Appl. Anal. Discrete Math. 7 (1), pp. 161–179.
  • G. Nemes (2014a) Error bounds and exponential improvement for the asymptotic expansion of the Barnes G -function. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 470 (2172), pp. 20140534, 14.
  • G. Nemes (2015b) On the large argument asymptotics of the Lommel function via Stieltjes transforms. Asymptot. Anal. 91 (3-4), pp. 265–281.