Skip to main content
SpringerLink
Log in

A note on error bounds for approximation in inner product spaces

  • Published:
Circuits, Systems and Signal Processing Aims and scope Submit manuscript

Abstract

In a recent paper a method is described for constructing certain approximations to a general element in the closure of the convex hull of a subset of an inner product space. This is of interest in connection with neural networks. Here we give an algorithm that generates simpler approximants with somewhat less computational cost.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. A. R. Barron, Universal approximation bounds for superpositions of a sigmoidal function,IEEE Transactions on Information Theory, vol. 39, no. 3, pp. 930–945, May 1993.

    Google Scholar 

  2. E. W. Cheney, Topics in approximation theory, Course Notes for Mathematics 393D, Department of Mathematics, The University of Texas at Austin, Spring 1993.

  3. G. Cybenko, Approximation by superposition of a single function,Mathematics of Control, Signals and Systems, vol. 2, pp. 303–314, 1989.

    Google Scholar 

  4. F. Girosi and G. Anzellotti, Rates of convergence for radial basis functions and neural networks,in Artificial Neural Networks with Applications in Speech and Vision, Chapman & Hall, 1993.

  5. L. K. Jones, A simple lemma on greedy approximation in Hilbert space and convergence rates for projection pursuit regression and neural network training,The Annals of Statistics, vol. 20, pp. 608–613, March 1992.

    Google Scholar 

  6. G. Pisier, Remarques sur un resultat non publie de B. Maurey,Seminaire d'Analyse Fonctionelle, vol. 1, no. 12, Ecole Polytechnique, Centre de Mathematiques, Palaiseau, 1980–81.

    Google Scholar 

  7. I. W. Sandberg, General structures for classification,IEEE Transactions on Circuits and Systems-I: Fundamental Theory and Applications, vol. 41, no. 5, pp. 372–376, May 1994.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. IBM Corporation, 11400 Burnet Road, 78758, Austin, Texas

    Ajit Dingankar

  2. Department of Electrical and Computer Engineering, The University of Texas at Austin, 78712, Austin, Texas

    Irwin W. Sandberg

Authors
  1. Ajit Dingankar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Irwin W. Sandberg
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dingankar, A., Sandberg, I.W. A note on error bounds for approximation in inner product spaces. Circuits Systems and Signal Process 15, 515–518 (1996). https://doi.org/10.1007/BF01183158

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01183158

Keywords

Search

Navigation