Package org.drip.numerical.quadrature

Class GolubWelsch

java.lang.Object
org.drip.numerical.quadrature.GolubWelsch
public class GolubWelsch
extends java.lang.Object
GolubWelsch implements the Golub-Welsch Algorithm that extracts the Quadrature Nodes and 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 Summary

    Constructors
    Constructor Description
    GolubWelsch​(double[][] recurrenceJ)
    GolubWelsch Constructor

  • Method Summary

    Modifier and Type Method Description
    Array2D nodesAndUnscaledWeights()
    Generate the Quadrature Nodes and Unscaled Weights
    double[][] recurrenceJ()
    Retrieve the Recurrence Matrix J
    double[][] symmetricTridiagonal()
    Generate the Symmetric Tri-diagonal Matrix from the Recurrence J Matrix

    Methods inherited from class java.lang.Object

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

  • Constructor Details

    • GolubWelsch

      public GolubWelsch​(double[][] recurrenceJ) throws java.lang.Exception
      GolubWelsch Constructor
      Parameters:
      recurrenceJ - The J Matrix derived from Orthogonal Polynomial Recursion
      Throws:
      java.lang.Exception - Thrown if the Inputs are Invalid

  • Method Details

    • recurrenceJ

      public double[][] recurrenceJ()
      Retrieve the Recurrence Matrix J
      Returns:
      The Recurrence Matrix J

    • symmetricTridiagonal

      public double[][] symmetricTridiagonal()
      Generate the Symmetric Tri-diagonal Matrix from the Recurrence J Matrix
      Returns:
      The Symmetric Tri-diagonal Matrix from the Recurrence J Matrix

    • nodesAndUnscaledWeights

      public Array2D nodesAndUnscaledWeights()
      Generate the Quadrature Nodes and Unscaled Weights
      Returns:
      The Quadrature Nodes and Unscaled Weights