Fundamentality of ridge functions

Journal of Approximation Theory

Volumn 75, Issue 3, 1993, Pages 295-311

  Lin, Vladimir Ya ^a   Pinkus, Allan ^a  

^a TECHNION ISRAEL INSTITUTE OF TECHNOLOGY   (Israel)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 38248999102     PISSN: 00219045     EISSN: None     Source Type: Journal    
DOI: 10.1006/jath.1993.1104     Document Type: Article

References (17)

1. D. BRAESS and A. PINKUS, Interpolation by ridge functions, J. Approx. Theory 73 (1993), 218-236.
2. C. K. CHCI and XIN LI, Approximation by ridge functions and neural networks with one hidden layer, J. Approx. Theory 70 (1992), 131-141.
3. G. CYBENKO, Approximation by superpositions of a sigmoidal function, Math. Control, Signals, Systems 2 (1989), 303-314.
4. W. Dahmen and C. A. Micchelli, Some remarks on ridge functions, Approx. Theory Appl. 3 (1987), 139-143.
5. P. Diaconis and M. Shahshahani, On nonlinear functions of linear combinations, SIAM J. Sci. Statist. Comput. Appl. 5 (1984), 175-191.
6. D. L. DONOHO and I. M. JOHNSTONE, Projection-based approximation and a duality method with kernel methods, Ann. Statist. 17 (1989), 58-106.
7. R. E. EDWARDS, "Functional Analysis, Theory and Applications, " Holt, Rinehart & Winston, New York, 1965.
8. C. HAMAKER and D. C. SOLOMON, The angles between the null spaces of -V'-rays, J. Math. Anal. Appl. 62 (1978), 1-23.
9. P. J. HUBER, Projection pursuit, Ann. Statist. 13 (1985), 435-475.
10. F. JOHN, "Plane Waves and Spherical Means Applied to Partial Differential Equations, " Interscience, New York, 1955.
11. L. LESHNO, V. YA. LIN, A. PINKUS, and S. SCHOCKEN, Multilayer feedforward networks with a non-polynomial activation function can approximate any function, Neural Networks, to appear.
12. B. F. LOGAN and L. A. SHEPP, Optimal reconstruction of a function from its projections, Duke Math. J. 42 (1975), 645-659.
13. F. NATTERER, "The Mathematics of Computerized Tomography, " Wiley, New York, 1986.
14. X. SUN and E. W. CHENEY, The fundamentality of sets of ridge functions, preprint.
15. B. A. VOSTRECOV and M. A. KREINES, Approximation of continuous functions by superpositions of plane waves, Doki. Akad. Nauk SSSR 140 (1961), 1237-1240 (Soviet Math. Dokl. 2 (1961), 1326-1329).
16. B. A. VOSTRECOV and M. A. KREINES, Approximation of a plane wave by superpositions of plane waves of given directions, Dokl. Akad. Nauk SSSR 144 (1962), 1212-1214 (Soviet Math. Dokl. 3 (1962), 875-877).
17. B. A. VOSTRECOV, Conditions for a function of many variables to be representable as a sum of a finite number of plane waves traveling in given directions, Dokl. Akad. Nauk SSSR 153 (1963), 16-19 (Soviet Math. Dokl. 4 (1963), 1588-1591).