Package org.drip.numerical.integration

Class GaussLobattoQuadratureGenerator

java.lang.Object
org.drip.numerical.integration.GaussLobattoQuadratureGenerator
public class GaussLobattoQuadratureGenerator
extends java.lang.Object
GaussLobattoQuadratureGenerator generates the Array of Orthogonal Lobatto Polynomial Gaussian Quadrature Based Abscissa and their corresponding Weights. The References are:

  • Abramowitz, M., and I. A. Stegun (2007): Handbook of Mathematics Functions Dover Book on Mathematics
  • Gil, A., J. Segura, and N. M. Temme (2007): Numerical Methods for Special Functions Society for Industrial and Applied Mathematics Philadelphia
  • Press, W. H., S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery (2007): Numerical Recipes: The Art of Scientific Computing 3rd Edition Cambridge University Press New York
  • Stoer, J., and R. Bulirsch (2002): Introduction to Numerical Analysis 3rd Edition Springer
  • Wikipedia (2019): Gaussian Quadrature https://en.wikipedia.org/wiki/Gaussian_quadrature


Author:
Lakshmi Krishnamurthy

  • Constructor Details

    • GaussLobattoQuadratureGenerator

      public GaussLobattoQuadratureGenerator()

  • Method Details

    • ThreePoint

      public static final QuadratureEstimator ThreePoint​(AbscissaTransform abscissaTransformer)
      Generate the Three Point Gauss Lobatto Quadrature over [-1, +1]
      Parameters:
      abscissaTransformer - The Abscissa Transformer
      Returns:
      The Three Point Gauss Lobatto Quadrature over [-1, +1]

    • FourPoint

      public static final QuadratureEstimator FourPoint​(AbscissaTransform abscissaTransformer)
      Generate the Four Point Gauss Lobatto Quadrature over [-1, +1]
      Parameters:
      abscissaTransformer - The Abscissa Transformer
      Returns:
      The Four Point Gauss Lobatto Quadrature over [-1, +1]

    • FivePoint

      public static final QuadratureEstimator FivePoint​(AbscissaTransform abscissaTransformer)
      Generate the Five Point Gauss Lobatto Quadrature over [-1, +1]
      Parameters:
      abscissaTransformer - The Abscissa Transformer
      Returns:
      The Five Point Gauss Lobatto Quadrature over [-1, +1]

    • SixPoint

      public static final QuadratureEstimator SixPoint​(AbscissaTransform abscissaTransformer)
      Generate the Six Point Gauss Lobatto Quadrature over [-1, +1]
      Parameters:
      abscissaTransformer - The Abscissa Transformer
      Returns:
      The Six Point Gauss Lobatto Quadrature over [-1, +1]

    • SevenPoint

      public static final QuadratureEstimator SevenPoint​(AbscissaTransform abscissaTransformer)
      Generate the Seven Point Gauss Lobatto Quadrature over [-1, +1]
      Parameters:
      abscissaTransformer - The Abscissa Transformer
      Returns:
      The Seven Point Gauss Lobatto Quadrature over [-1, +1]

    • ThreePoint

      public static final QuadratureEstimator ThreePoint​(double left, double right)
      Generate the Three Point Gauss Legendre Quadrature over [a, b] onto [-1, +1]
      Parameters:
      left - Left Integrand Quadrature Limit
      right - Right Integrand Quadrature Limit
      Returns:
      The Three Point Gauss Legendre Quadrature over [a, b] onto [-1, +1]

    • FourPoint

      public static final QuadratureEstimator FourPoint​(double left, double right)
      Generate the Four Point Gauss Legendre Quadrature over [a, b] onto [-1, +1]
      Parameters:
      left - Left Integrand Quadrature Limit
      right - Right Integrand Quadrature Limit
      Returns:
      The Four Point Gauss Legendre Quadrature over [a, b] onto [-1, +1]

    • FivePoint

      public static final QuadratureEstimator FivePoint​(double left, double right)
      Generate the Five Point Gauss Legendre Quadrature over [a, b] onto [-1, +1]
      Parameters:
      left - Left Integrand Quadrature Limit
      right - Right Integrand Quadrature Limit
      Returns:
      The Five Point Gauss Legendre Quadrature over [a, b] onto [-1, +1]

    • SixPoint

      public static final QuadratureEstimator SixPoint​(double left, double right)
      Generate the Six Point Gauss Legendre Quadrature over [a, b] onto [-1, +1]
      Parameters:
      left - Left Integrand Quadrature Limit
      right - Right Integrand Quadrature Limit
      Returns:
      The Six Point Gauss Legendre Quadrature over [a, b] onto [-1, +1]

    • SevenPoint

      public static final QuadratureEstimator SevenPoint​(double left, double right)
      Generate the Seven Point Gauss Legendre Quadrature over [a, b] onto [-1, +1]
      Parameters:
      left - Left Integrand Quadrature Limit
      right - Right Integrand Quadrature Limit
      Returns:
      The Seven Point Gauss Legendre Quadrature over [a, b] onto [-1, +1]