Class AbramowitzStegun


public abstract class AbramowitzStegun
extends ErrorFunction
AbramowitzStegun implements the E2 (erf) Estimator using Abramowitz-Stegun Scheme. The References are:

  • Abramowitz, M., and I. A. Stegun (2007): Handbook of Mathematics Functions Dover Book on Mathematics
  • Chang, S. H., P. C. Cosman, L. B. Milstein (2011): Chernoff-Type Bounds for Gaussian Error Function IEEE Transactions on Communications 59 (11) 2939-2944
  • Cody, W. J. (1991): Algorithm 715: SPECFUN – A Portable FORTRAN Package of Special Function Routines and Test Drivers ACM Transactions on Mathematical Software 19 (1) 22-32
  • Schopf, H. M., and P. H. Supancic (2014): On Burmann’s Theorem and its Application to Problems of Linear and Non-linear Heat Transfer and Diffusion https://www.mathematica-journal.com/2014/11/on-burmanns-theorem-and-its-application-to-problems-of-linear-and-nonlinear-heat-transfer-and-diffusion/#more-39602/
  • Wikipedia (2019): Error Function https://en.wikipedia.org/wiki/Error_function


Author:
Lakshmi Krishnamurthy
  • Constructor Details

    • AbramowitzStegun

      public AbramowitzStegun​(AbramowitzStegunSeriesGenerator abramowitzStegunSeriesGenerator, DerivativeControl dc, double maximumError) throws java.lang.Exception
      E2AbramowitzStegun Constructor
      Parameters:
      abramowitzStegunSeriesGenerator - Abramowitz Stegun Series Generator
      dc - The Derivative Control
      maximumError - Maximum Error
      Throws:
      java.lang.Exception - Thrown if the Inputs are Invalid
  • Method Details

    • InversePolynomial4

      public static final AbramowitzStegun InversePolynomial4()
      Construct the Inverse Degree 4 Polynomial Version of Abramowitz-Stegun E2 erf Estimator
      Returns:
      The Inverse Degree 4 Polynomial Version of Abramowitz-Stegun E2 erf Estimator
    • MixedPolynomial3

      public static final AbramowitzStegun MixedPolynomial3()
      Construct the Mixed Degree 3 Polynomial Version of Abramowitz-Stegun E2 erf Estimator
      Returns:
      The Mixed Degree 3 Polynomial Version of Abramowitz-Stegun E2 erf Estimator
    • InversePolynomial6

      public static final AbramowitzStegun InversePolynomial6()
      Construct the Inverse Degree 6 Polynomial Version of Abramowitz-Stegun E2 erf Estimator
      Returns:
      The Inverse Degree 6 Polynomial Version of Abramowitz-Stegun E2 erf Estimator
    • MixedPolynomial5

      public static final AbramowitzStegun MixedPolynomial5()
      Construct the Mixed Degree 5 Polynomial Version of Abramowitz-Stegun E2 erf Estimator
      Returns:
      The Mixed Degree 5 Polynomial Version of Abramowitz-Stegun E2 erf Estimator
    • NumericalRecipe2007

      public static final AbramowitzStegun NumericalRecipe2007()
      Construct the Numerical Recipe Version of Abramowitz-Stegun E2 erf Estimator
      Returns:
      The Numerical Recipe Version of Abramowitz-Stegun E2 erf Estimator
    • maximumError

      public double maximumError()
      Retrieve the Maximum Error
      Returns:
      The Maximum Error