Approximation properties of zonal function networks using scattered data on the sphere

Advances in Computational Mathematics

Volumn 11, Issue 2-3, 1999, Pages 121-137

  Mhaskar, H N ^a   Narcowich, F J ^b   Ward, J D ^b  

^a CALIFORNIA STATE UNIVERSITY   (United States)

^b TEXAS A AND M UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033460583     PISSN: 10197168     EISSN: None     Source Type: Journal    
DOI: 10.1023/a:1018967708053     Document Type: Article

References (15)

1. R. DeVore, R. Howard and C.A. Micchelli, Optimal nonlinear approximation, Manuscripta Math. 63 (1989) 469-478.
2. R. DeVore and G.G. Lorentz, Constructive Approximation (Springer, Berlin, 1994).
3. K. Jetter, J. Stöckler and J.D. Ward, Error estimates for scattered data interpolation, Math. Comp. 68 (1999) 743-747.
4. G.G. Lorentz, Approximation of Functions (Holt, Rinehart and Winston, New York, 1966).
5. H.N. Mhaskar, Approximation of smooth functions by neural networks, in: Dealing with Complexity: A Neural Network Approach, eds. K. Warwick, V. Kurkova and M. Karny (Springer, Berlin, 1997) pp. 189-204.
6. H.N. Mhaskar and C.A. Micchelli, Degree of approximation by neural and translation networks with a single hidden layer, Adv. Appl. Math. 16 (1995) 151-183.
7. H.N. Mhaskar, F.J. Narcowich and J.D. Ward, Spherical Marcinkiewicz-Zygmund inequalities and positive quadrature, Math. Comp., to appear.
8. H.N. Mhaskar and J. Prestin, Marcinkiewicz-Zygmund-type inequalities, in: Approximation Theory: In Memory of A.K. Varma, eds. N.K. Govil, R.N. Mohapatra, Z. Nashed, A. Sharma and J. Szabados (Marcel Dekker, New York, 1998).
9. C. Müller, Spherical Harmonics, Lecture Notes in Mathematics, Vol. 17 (Springer, Berlin, 1966).
10. S. Pawelke, Über die Approximationsordnung bei Kugelfunktionen und algebraischen Polynomen, Tôhoku Math. J. 24 (1972) 473-486.
11. A. Pinkus, n-widths in Approximation Theory (Springer, New York, 1985).
12. E.M. Stein, Interpolation in polynomial classes and Markoff's inequality, Duke Math. J. 24 (1957) 467-476.
13. E.M. Stein and G. Weiss, Fourier Analysis on Euclidean Spaces (Princeton University Press, Princeton, NJ, 1971).
14. G. Szegö, Orthogonal Polynomials, American Mathematical Society Colloquium Publications, Vol. 23 (Amer. Math. Soc., Providence, RI, 1975).
15. E.T. Whittaker and G.N. Watson, A Course of Modern Analysis (Cambridge University Press, Cambridge, 1965).