Package org.drip.numerical.integration

Class GaussKronrodQuadratureGenerator

java.lang.Object
org.drip.numerical.integration.GaussKronrodQuadratureGenerator
public class GaussKronrodQuadratureGenerator
extends java.lang.Object
GaussKronrodQuadratureGenerator generates the Array of Gaussian Quadrature Based Abscissa and their corresponding Weights, with the Kronrod Extensions applied. The References are:

  • Holoborodko, P. (2011): Gauss-Kronrod Quadrature Nodes and Weights https://www.advanpix.com/2011/11/07/gauss-kronrod-quadrature-nodes-weights/
  • Kahaner, D., C. Moler, and S. Nash (1989): Numerical Methods and Software Prentice Hall
  • Laurie, D. (1997): Calculation of Gauss-Kronrod Quadrature Rules Mathematics of Computation 66 (219) 1133-1145
  • Piessens, R., E. de Doncker-Kapenga, C. W. Uberhuber, and D. K. Kahaner (1983): QUADPACK – A Subroutine Package for Automatic Integration Springer-Verlag
  • Wikipedia (2019): Gauss-Kronrod Quadrature Formula https://en.wikipedia.org/wiki/Gauss%E2%80%93Kronrod_quadrature_formula


Author:
Lakshmi Krishnamurthy

  • Constructor Summary

    Constructors
    Constructor Description
    GaussKronrodQuadratureGenerator()  

  • Method Summary

    Modifier and Type Method Description
    static QuadratureEstimator G7​(double left, double right)
    Generate the Nested/Embedded G7 Gaussian Quadrature over (a, b) onto (-1, +1)
    static QuadratureEstimator G7​(AbscissaTransform abscissaTransformer)
    Generate the Nested/Embedded G7 Gaussian Quadrature over (0, +1)
    static NestedQuadratureEstimator G7K15​(double left, double right)
    Generate the G7-K15 Nested Quadrature Estimator over (a, b) onto (-1, +1)
    static QuadratureEstimator K15​(double left, double right)
    Generate the K15 Gaussian Quadrature over (a, b) onto (-1, +1)
    static QuadratureEstimator K15​(AbscissaTransform abscissaTransformer)
    Generate the K15 Gaussian Quadrature over (0, +1)

    Methods inherited from class java.lang.Object

    equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

  • Constructor Details

    • GaussKronrodQuadratureGenerator

      public GaussKronrodQuadratureGenerator()

  • Method Details

    • G7

      public static final QuadratureEstimator G7​(AbscissaTransform abscissaTransformer)
      Generate the Nested/Embedded G7 Gaussian Quadrature over (0, +1)
      Parameters:
      abscissaTransformer - The Abscissa Transformer
      Returns:
      The Nested/Embedded G7 Gaussian Quadrature over (0, +1)

    • K15

      public static final QuadratureEstimator K15​(AbscissaTransform abscissaTransformer)
      Generate the K15 Gaussian Quadrature over (0, +1)
      Parameters:
      abscissaTransformer - The Abscissa Transformer
      Returns:
      The K15 Gaussian Quadrature over (0, +1)

    • G7

      public static final QuadratureEstimator G7​(double left, double right)
      Generate the Nested/Embedded G7 Gaussian Quadrature over (a, b) onto (-1, +1)
      Parameters:
      left - Left Integrand Quadrature Limit
      right - Right Integrand Quadrature Limit
      Returns:
      The Nested/Embedded G7 Gaussian Quadrature over (a, b) onto (-1, +1)

    • K15

      public static final QuadratureEstimator K15​(double left, double right)
      Generate the K15 Gaussian Quadrature over (a, b) onto (-1, +1)
      Parameters:
      left - Left Integrand Quadrature Limit
      right - Right Integrand Quadrature Limit
      Returns:
      The K15 Gaussian Quadrature over (a, b) onto (-1, +1)

    • G7K15

      public static final NestedQuadratureEstimator G7K15​(double left, double right)
      Generate the G7-K15 Nested Quadrature Estimator over (a, b) onto (-1, +1)
      Parameters:
      left - Left Integrand Quadrature Limit
      right - Right Integrand Quadrature Limit
      Returns:
      The G7-K15 Nested Quadrature Estimator over (a, b) onto (-1, +1)