Random approximants and neural networks

Journal of Approximation Theory

Volumn 85, Issue 1, 1996, Pages 98-109

  Makovoz, Y ^a  

^a UNIVERSITY OF MASSACHUSETTS LOWELL   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030119952     PISSN: 00219045     EISSN: None     Source Type: Journal    
DOI: 10.1006/jath.1996.0031     Document Type: Article

References (13)

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4. 3. E. S. BELINSKII, Approximation by a "floating" system of exponentials on classes of smooth periodic functions, Mat. Sb. 132, No. 1 (1987); Mat. USSR Sb. 60, No. 1 (1988), 19-27.
5. 4. G. CYBENKO, Approximations by superpositions of a sigmoidal function, Math. Control, Signal, Systems 2 (1989), 303-314.
6. 5. C. DARKEN, M. DONAHUE, L. GURVITS, AND E. SONTAG, Rate of approximation results motivated by robust neural network learning, extended abstract of Siemens Technical Report LS93-07, Siemens, 1993.
7. 6. L. K. JONES, Constructive approximations for neural networks by sigmoidal functions, Proc. IEEE 78, No. 10 (1990), 1586-1589.
8. 7. L. K. JONES, A simple lemma on greedy approximation in Hilbert space and convergence rates for projection pursuit regression and neural networking training, Ann. of Statist. 20 (1992), 608-613.
9. 8. P. LANKASTER, "Theory of Matrices," Academic Press, New York, 1969.
10. 9. G. G. LORENTZ, Metric entropy and approximation, Bull. Amer. Math. Soc. 72 (1966), 903-937
11. 10. Y. MAKOVOZ, On trigonometric n-widths and their generalization, J. Approx. Theory 41, No. 4 (1984), 361-366.
12. 11. G. PISIER, Remarques sur un résultat non publié de B. Maurey, in "Séminaire d'analyse fonctionelle 1980-1981, École Polytechnique, Centre de Mathématiques, Palaiseau."
13. 12. A. ZYGMUND, "Trigonometric Series," Cambridge Univ. Press, Cambridge, 1959.