메뉴 건너뛰기




Volumn 22, Issue 3, 2006, Pages 348-370

Weighted quadrature formulas and approximation by zonal function networks on the sphere

Author keywords

Approximation on the sphere; Neural networks; Quadrature formulas; Radial basis functions; Spherical basis functions

Indexed keywords

ERRORS; FUNCTION EVALUATION; NEURAL NETWORKS; NONLINEAR SYSTEMS; POLYNOMIAL APPROXIMATION;

EID: 33646842350     PISSN: 0885064X     EISSN: 10902708     Source Type: Journal    
DOI: 10.1016/j.jco.2005.10.003     Document Type: Article
Times cited : (39)

References (32)
  • 1
    • 0027599793 scopus 로고
    • Universal approximation bounds for superpositions of a sigmoidal function
    • Barron A.R. Universal approximation bounds for superpositions of a sigmoidal function. IEEE Trans. Inform. Theory 39 (1993) 930-945
    • (1993) IEEE Trans. Inform. Theory , vol.39 , pp. 930-945
    • Barron, A.R.1
  • 2
    • 33646826875 scopus 로고    scopus 로고
    • J.S. Brauchart, K. Hesse, Numerical integration over spheres of arbitrary dimension, Applied Mathematics Report AMR05/7, The University of New South Wales, March 2005.
  • 3
    • 13644283759 scopus 로고    scopus 로고
    • Approximation of smooth functions on compact two-point homogeneous spaces
    • Brown G., and Dai F. Approximation of smooth functions on compact two-point homogeneous spaces. J. Funct. Anal. 220 2 (2005) 401-423
    • (2005) J. Funct. Anal. , vol.220 , Issue.2 , pp. 401-423
    • Brown, G.1    Dai, F.2
  • 5
    • 33646841376 scopus 로고    scopus 로고
    • F. Dai, On generalized hyperinterpolation on the sphere, manuscript.
  • 6
    • 0000273884 scopus 로고
    • Computing Fourier transforms and convolutions for the 2-sphere
    • Driscoll J.R., and Healy D.M. Computing Fourier transforms and convolutions for the 2-sphere. Adv. Appl. Math. 15 (1994) 202-250
    • (1994) Adv. Appl. Math. , vol.15 , pp. 202-250
    • Driscoll, J.R.1    Healy, D.M.2
  • 9
    • 33646823009 scopus 로고    scopus 로고
    • Q.T. Le Gia, H.N. Mhaskar, Polynomial operators and local approximation of solutions of pseudo-differential equations on the sphere, submitted for publication. (http://www.calstatela.edu/faculty/hmhaska/postscript/psdiff.pdf)
  • 10
    • 33646854585 scopus 로고    scopus 로고
    • K. Hesse, A lower bound for the worst-case cubature error on spheres on arbitrary dimensions, preprint.
  • 11
    • 33646851943 scopus 로고    scopus 로고
    • 2 in Sobolev spaces of arbitrary order, Applied Mathematics Report AMR 4/27, The University of New South Wales, Sydney, Australia, August, 2004.
  • 12
    • 27844500239 scopus 로고    scopus 로고
    • 2, J. Complexity 21(6) (2005) 790-803.
  • 13
    • 0005611244 scopus 로고    scopus 로고
    • Norming sets and spherical cubature formulas
    • Li C., Micchelli C., and Xu Y. (Eds), Marcel Dekker, New York
    • Jetter K., Stöckler J., and Ward J.D. Norming sets and spherical cubature formulas. In: Li C., Micchelli C., and Xu Y. (Eds). Computational Mathematics (1998), Marcel Dekker, New York 237-245
    • (1998) Computational Mathematics , pp. 237-245
    • Jetter, K.1    Stöckler, J.2    Ward, J.D.3
  • 14
    • 0035443484 scopus 로고    scopus 로고
    • Bounds on rates of variable basis and neural network approximation
    • Kurkova V., and Sanguineti M. Bounds on rates of variable basis and neural network approximation. IEEE Trans. Inform. Theory 47 (2001) 2659-2665
    • (2001) IEEE Trans. Inform. Theory , vol.47 , pp. 2659-2665
    • Kurkova, V.1    Sanguineti, M.2
  • 15
    • 3242701678 scopus 로고    scopus 로고
    • On the tractability of multivariate integration and approximation by neural networks
    • Mhaskar H.N. On the tractability of multivariate integration and approximation by neural networks. J. Complexity 20 (2004) 561-590
    • (2004) J. Complexity , vol.20 , pp. 561-590
    • Mhaskar, H.N.1
  • 16
    • 10944228037 scopus 로고    scopus 로고
    • Polynomial operators and local smoothness classes on the unit interval
    • Mhaskar H.N. Polynomial operators and local smoothness classes on the unit interval. J. Approx. Theory 131 (2004) 243-267
    • (2004) J. Approx. Theory , vol.131 , pp. 243-267
    • Mhaskar, H.N.1
  • 17
    • 16344364530 scopus 로고    scopus 로고
    • On the representation of smooth functions on the sphere using finitely many bits
    • Mhaskar H.N. On the representation of smooth functions on the sphere using finitely many bits. Appl. Comput. Harmonic Anal. 18 3 (2005) 215-233
    • (2005) Appl. Comput. Harmonic Anal. , vol.18 , Issue.3 , pp. 215-233
    • Mhaskar, H.N.1
  • 18
    • 0035608775 scopus 로고    scopus 로고
    • Spherical Marcinkiewicz-Zygmund inequalities and positive quadrature
    • (Corrigendum: Math. Comp. 71 (2001) 453-454)
    • Mhaskar H.N., Narcowich F.J., and Ward J.D. Spherical Marcinkiewicz-Zygmund inequalities and positive quadrature. Math. Comp. 70 235 (2001) 1113-1130 (Corrigendum: Math. Comp. 71 (2001) 453-454)
    • (2001) Math. Comp. , vol.70 , Issue.235 , pp. 1113-1130
    • Mhaskar, H.N.1    Narcowich, F.J.2    Ward, J.D.3
  • 19
    • 0033460583 scopus 로고    scopus 로고
    • Approximation properties of zonal function networks using scattered data on the sphere
    • Mhaskar H.N., Narcowich F.J., and Ward J.D. Approximation properties of zonal function networks using scattered data on the sphere. Adv. Comput. Math. 11 (1999) 121-137
    • (1999) Adv. Comput. Math. , vol.11 , pp. 121-137
    • Mhaskar, H.N.1    Narcowich, F.J.2    Ward, J.D.3
  • 21
    • 0030221021 scopus 로고    scopus 로고
    • An integral representation of functions using three-layered networks and their approximation bounds
    • Murata N. An integral representation of functions using three-layered networks and their approximation bounds. Neural Networks 9 (1996) 947-956
    • (1996) Neural Networks , vol.9 , pp. 947-956
    • Murata, N.1
  • 22
    • 33646853347 scopus 로고    scopus 로고
    • F.J. Narcowich, P. Petrushev, J.D. Ward, Localized tight frames on spheres, manuscript.
  • 23
    • 0036433867 scopus 로고    scopus 로고
    • Scattered data interpolation on spheres: error estimates and locally supported basis functions
    • Narcowich F.J., and Ward J.D. Scattered data interpolation on spheres: error estimates and locally supported basis functions. SIAM J. Math. Anal. 33 6 (2002) 1393-1410
    • (2002) SIAM J. Math. Anal. , vol.33 , Issue.6 , pp. 1393-1410
    • Narcowich, F.J.1    Ward, J.D.2
  • 26
    • 0032283665 scopus 로고    scopus 로고
    • Approximation by ridge functions and neural networks
    • Petrushev P. Approximation by ridge functions and neural networks. SIAM J. Math. Anal. 30 (1998) 155-189
    • (1998) SIAM J. Math. Anal. , vol.30 , pp. 155-189
    • Petrushev, P.1
  • 27
    • 0032367851 scopus 로고    scopus 로고
    • Fast algorithms for discrete polynomial transforms
    • Potts D., Steidl G., and Tasche M. Fast algorithms for discrete polynomial transforms. Math. Comp. 67 (1998) 1577-1590
    • (1998) Math. Comp. , vol.67 , pp. 1577-1590
    • Potts, D.1    Steidl, G.2    Tasche, M.3
  • 28
    • 33646839652 scopus 로고    scopus 로고
    • Approximation by positive definite kernels
    • Buhmann M.D., and Mache D.H. (Eds), Birkhäuser Verlag
    • Schaback R., and Wendland H. Approximation by positive definite kernels. In: Buhmann M.D., and Mache D.H. (Eds). Advanced Problems in Constructive Approximation, ISNM vol. 142 (2002), Birkhäuser Verlag 203-221
    • (2002) Advanced Problems in Constructive Approximation, ISNM , vol.142 , pp. 203-221
    • Schaback, R.1    Wendland, H.2
  • 31
    • 33646837887 scopus 로고    scopus 로고
    • G. Szegö, Orthogonal Polynomials, American Mathematical Society Colloquium Publishers, vol. 23, American Mathematical Society, Providence, RI, 1975.


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.