Bochner Integrals and Neural Networks View Full Text


Ontology type: schema:Chapter     


Chapter Info

DATE

2013

AUTHORS

Paul C. Kainen , Andrew Vogt

ABSTRACT

A Bochner integral formula \(f = \mathcal{B}-\int_Y w(y)\Phi(y) d\mu(y)\) is derived that presents a function f in terms of weights w and a parametrized family of functions Φ(y), y in Y . Comparison is made to pointwise formulations, norm inequalities relating pointwise and Bochner integrals are established, G-variation and tensor products are studied, and examples are presented. More... »

PAGES

183-214

References to SciGraph publications

  • 1997. Dimension-Independent Rates of Approximation by Neural Networks in COMPUTER INTENSIVE METHODS IN CONTROL AND SIGNAL PROCESSING
  • 2010-04. Estimates of Variation with Respect to a Set and Applications to Optimization Problems in JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
  • 2009-01. Approximation Schemes for Functional Optimization Problems in JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS
  • 2007. A Concise Course on Stochastic Partial Differential Equations in NONE
  • 1965. Real and Abstract Analysis, A modern treatment of the theory of functions of a real variable in NONE
  • 2009. Model Complexity of Neural Networks and Integral Transforms in ARTIFICIAL NEURAL NETWORKS – ICANN 2009
  • 1985. Stochastic Control in STOCHASTIC CONTROL. ÜBER DEN EMPIRISCHEN GEHALT DER NEOKLASSISCHEN ÖKONOMISCHEN THEORIE
  • Book

    TITLE

    Handbook on Neural Information Processing

    ISBN

    978-3-642-36656-7
    978-3-642-36657-4

    Author Affiliations

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/978-3-642-36657-4_6

    DOI

    http://dx.doi.org/10.1007/978-3-642-36657-4_6

    DIMENSIONS

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