org.drip.spaces.functionclass

Class HilbertRxToSupremumRdFinite

java.lang.Object

org.drip.spaces.functionclass.NormedRxToNormedRxFinite

org.drip.spaces.functionclass.NormedRxToNormedRdFinite

org.drip.spaces.functionclass.HilbertRxToSupremumRdFinite

public class HilbertRxToSupremumRdFinite
extends NormedRxToNormedRdFinite

HilbertRxToSupremumRdFinite implements the Class F with f E f : Hilbert R^x To Supremum R^d Space of Finite Functions. 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
HilbertRxToSupremumRdFinite(double dblMaureyConstant, NormedRxToNormedRd[] aHilbertRxToSupremumRd) HilbertRxToSupremumRdFinite Constructor

Method Summary

Methods inherited from class org.drip.spaces.functionclass.NormedRxToNormedRdFinite

agnosticCoveringNumberBounds, functionSpaces, inputMetricVectorSpace, operatorPopulationMetricNorm, operatorPopulationSupremumNorm, operatorSampleMetricNorm, operatorSampleSupremumNorm, outputMetricVectorSpace, populationCoveringNumber, populationCoveringNumber, populationRdMetricNorm, populationRdSupremumNorm, populationSupremumCoveringNumber, populationSupremumCoveringNumber, sampleCoveringNumber, sampleCoveringNumber, sampleRdMetricNorm, sampleRdSupremumNorm, sampleSupremumCoveringNumber, sampleSupremumCoveringNumber

Methods inherited from class org.drip.spaces.functionclass.NormedRxToNormedRxFinite

maureyConstant, outputDimension, populationMetricCoveringBounds, populationSupremumCoveringBounds, sampleMetricCoveringBounds, sampleSupremumCoveringBounds, scaleSensitiveCoveringBounds

Methods inherited from class java.lang.Object

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

Constructor Detail

HilbertRxToSupremumRdFinite

public HilbertRxToSupremumRdFinite(double dblMaureyConstant,
                                   NormedRxToNormedRd[] aHilbertRxToSupremumRd)
                            throws java.lang.Exception

HilbertRxToSupremumRdFinite Constructor

Parameters:

dblMaureyConstant - Maurey Constant

aHilbertRxToSupremumRd - Array of the Hilbert R^x To Supremum R^d Spaces

Throws:

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