Package org.drip.numerical.integration

Class NestedQuadratureEstimator

java.lang.Object

org.drip.numerical.integration.QuadratureEstimator

org.drip.numerical.integration.NestedQuadratureEstimator

public class NestedQuadratureEstimator
extends QuadratureEstimator

NestedQuadratureEstimator extends the R¹ Quadrature Estimator by providing the Estimation Error. The References are:

• Briol, F. X., C. J. Oates, M. Girolami, and M. A. Osborne (2015): Frank-Wolfe Bayesian Quadrature: Probabilistic Integration with Theoretical Guarantees arXiv
• Forsythe, G. E., M. A. Malcolm, and C. B. Moler (1977): Computer Methods for Mathematical Computation Prentice Hall Englewood Cliffs NJ
• Leader, J. J. (2004): Numerical Analysis and Scientific Computation Addison Wesley
• Stoer, J., and R. Bulirsch (1980): Introduction to Numerical Analysis Springer-Verlag New York
• Wikipedia (2019): Numerical Integration https://en.wikipedia.org/wiki/Numerical_integration

• Module = Computational Core Module
• Library = Numerical Analysis Library
• Project = Numerical Quadrature, Differentiation, Eigenization, Linear Algebra, and Utilities
• Package = R¹ R^d Numerical Integration Schemes

Author:

Lakshmi Krishnamurthy

Constructor Summary

Constructors

Constructor	Description
NestedQuadratureEstimator(AbscissaTransform abscissaTransformer, Array2D nodeWeightArray, QuadratureEstimator embeddedQuadratureEstimator)	NestedQuadratureEstimator Constructor

Method Summary

Modifier and Type	Method	Description
QuadratureEstimator	embeddedQuadratureEstimator()	Retrieve the Embedded Quadrature Estimator
QuadratureEstimate	estimate(R1ToR1 r1ToR1Integrand)	Estimate the Quadrature and its Error

Methods inherited from class org.drip.numerical.integration.QuadratureEstimator

abscissaTransform, integrate, nodeWeightArray

Methods inherited from class java.lang.Object

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

Constructor Details

NestedQuadratureEstimator

public NestedQuadratureEstimator(AbscissaTransform abscissaTransformer,
Array2D nodeWeightArray,
QuadratureEstimator embeddedQuadratureEstimator)
                          throws java.lang.Exception

NestedQuadratureEstimator Constructor

Parameters:

abscissaTransformer - The Abscissa Transformer

nodeWeightArray - Array of the Nodes and Weights

embeddedQuadratureEstimator - The Embedded Quadrature Estimator

Throws:

java.lang.Exception - Thrown if the Inputs are Invalid

Method Details

embeddedQuadratureEstimator

public QuadratureEstimator embeddedQuadratureEstimator()

Retrieve the Embedded Quadrature Estimator

Returns:

The Embedded Quadrature Estimator

estimate

public QuadratureEstimate estimate(R1ToR1 r1ToR1Integrand)

Estimate the Quadrature and its Error

Parameters:

r1ToR1Integrand - The R¹ To R¹ Integrand

Returns:

The Quadrature and its Error