org.drip.spaces.cover

Class CarlStephaniNormedBounds

java.lang.Object

org.drip.spaces.cover.CarlStephaniNormedBounds

public class CarlStephaniNormedBounds
extends java.lang.Object

CarlStephaniNormedBounds contains the Normed Bounds that result from the Convolution Product of 2 Normed R^x To Normed R^x Function Spaces. The References are: 1) Carl, B. (1985): Inequalities of the Bernstein-Jackson type and the Degree of Compactness of Operators in Banach Spaces, Annals of the Fourier Institute 35 (3) 79-118. 2) Carl, B., and I. Stephani (1990): Entropy, Compactness, and the Approximation of Operators, Cambridge University Press, Cambridge UK. 3) Williamson, R. C., A. J. Smola, and B. Scholkopf (2000): Entropy Numbers of Linear Function Classes, in: Proceedings of the 13th Annual Conference on Computational Learning Theory, ACM New York.

Author:

Lakshmi Krishnamurthy

Constructor Summary

Constructors

Constructor and Description
CarlStephaniNormedBounds(double dblEntropyBoundNormA, double dblEntropyBoundNormB) CarlStephaniNormedBounds Constructor

Method Summary

Modifier and Type	Method and Description
double	entropyBoundNormA() Retrieve the Entropy Bound using the Function Class Norm A
double	entropyBoundNormB() Retrieve the Entropy Bound using the Function Class Norm B
double	minimumUpperBound() Retrieve the Minimum Upper Entropy Bound

Methods inherited from class java.lang.Object

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

Constructor Detail

CarlStephaniNormedBounds

public CarlStephaniNormedBounds(double dblEntropyBoundNormA,
                                double dblEntropyBoundNormB)
                         throws java.lang.Exception

CarlStephaniNormedBounds Constructor

Parameters:

dblEntropyBoundNormA - The Entropy Bound using the Function Class Norm A

dblEntropyBoundNormB - The Entropy Bound using the Function Class Norm B

Throws:

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

Method Detail

entropyBoundNormA

public double entropyBoundNormA()

Retrieve the Entropy Bound using the Function Class Norm A

Returns:

The Entropy Bound using the Function Class Norm A

entropyBoundNormB

public double entropyBoundNormB()

Retrieve the Entropy Bound using the Function Class Norm B

Returns:

The Entropy Bound using the Function Class Norm B

minimumUpperBound

public double minimumUpperBound()

Retrieve the Minimum Upper Entropy Bound

Returns:

The Minimum Upper Entropy Bound