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Volumn 36, Issue 1, 2005, Pages 284-300

Scattered-data interpolation on ℝ n: Error estimates for radial basis and band-limited functions

Author keywords

Band limited functions; Error estimates; Interpolation; Radial basis functions; Scattered data

Indexed keywords

BAND-LIMITED FUNCTIONS; ERROR ESTIMATES; RADIAL BASIS FUNCTIONS; SCATTERED DATA;

EID: 14544277941     PISSN: 00361410     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036141002413579     Document Type: Article
Times cited : (52)

References (25)
  • 1
  • 2
    • 0035570177 scopus 로고    scopus 로고
    • Nonuniform sampling and reconstruction in shift-invariant spaces
    • A. ALDROUBI AND K. GRÖCHENIG, Nonuniform sampling and reconstruction in shift-invariant spaces, SIAM Rev., 43 (2001), pp. 585-620.
    • (2001) SIAM Rev. , vol.43 , pp. 585-620
    • Aldroubi, A.1    Gröchenig, K.2
  • 3
    • 0035541165 scopus 로고    scopus 로고
    • Fast evaluation of radial basis functions: Methods for four-dimensional polyharmonic splines
    • R. K. BEATSON, J. B. CHERRIE, AND D. L. RAGOZIN, Fast evaluation of radial basis functions: Methods for four-dimensional polyharmonic splines, SIAM J. Math. Anal. 32 (2001), pp. 1272-1310.
    • (2001) SIAM J. Math. Anal. , vol.32 , pp. 1272-1310
    • Beatson, R.K.1    Cherrie, J.B.2    Ragozin, D.L.3
  • 5
    • 0001142946 scopus 로고
    • Intermediate spaces and interpolation, the complex method
    • A. P. CALDERÓN, Intermediate spaces and interpolation, the complex method, Studia Math., 24 (1964), pp. 113-190.
    • (1964) Studia Math. , vol.24 , pp. 113-190
    • Calderón, A.P.1
  • 7
    • 0001935440 scopus 로고
    • Splines minimizing rotation invariant semi-norms in Sobolev spaces
    • Constructive Theory of Functions of Several Variables, W. Schempp and K. Zeller, eds., Springer, Berlin
    • J. DUCHON, Splines minimizing rotation invariant semi-norms in Sobolev spaces, in Constructive Theory of Functions of Several Variables, Lecture Notes in Math. 571, W. Schempp and K. Zeller, eds., Springer, Berlin, 1977, pp. 85-100.
    • (1977) Lecture Notes in Math. , vol.571 , pp. 85-100
    • Duchon, J.1
  • 9
    • 0001337147 scopus 로고
    • On some convergence properties of the interpolation polynomials
    • P. ERDÖS, On some convergence properties of the interpolation polynomials, Ann. of Math. (2), 44 (1943), pp. 330-337.
    • (1943) Ann. of Math. (2) , vol.44 , pp. 330-337
    • Erdös, P.1
  • 10
    • 0003292476 scopus 로고
    • Littlewood-Paley theory and the study of function spaces
    • AMS, Providence, RI
    • M. FRAZIER, B. JAWERTH, AND G. WEISS, Littlewood-Paley Theory and the Study of Function Spaces, CBMS Reg. Conf. Ser. Math. 79, AMS, Providence, RI, 1991.
    • (1991) CBMS Reg. Conf. Ser. Math. , vol.79
    • Frazier, M.1    Jawerth, B.2    Weiss, G.3
  • 13
    • 84966244353 scopus 로고
    • Multivariate interpolation and conditionally positive definite functions
    • W. R. MADYCH AND S. A. NELSON, Multivariate interpolation and conditionally positive definite functions. II, Math. Comp., 54 (1990), pp. 211-230.
    • (1990) II, Math. Comp. , vol.54 , pp. 211-230
    • Madych, W.R.1    Nelson, S.A.2
  • 15
    • 0040146904 scopus 로고
    • Norms of inverses and condition numbers for matrices associated with scattered data
    • F. J. NARCOWICH AND J. D. WARD, Norms of inverses and condition numbers for matrices associated with scattered data, J. Approx. Theory, 64 (1991), pp. 69-94.
    • (1991) J. Approx. Theory , vol.64 , pp. 69-94
    • Narcowich, F.J.1    Ward, J.D.2
  • 16
    • 38249012211 scopus 로고
    • Norm estimates for the inverses of a general class of scattered-data radial-function interpolation matrices
    • F. J. NARCOWICH AND J. D. WARD, Norm Estimates for the Inverses of a General Class of Scattered-Data Radial-Function Interpolation Matrices, J. Approx. Theory, 69 (1992), pp. 84-109.
    • (1992) J. Approx. Theory , vol.69 , pp. 84-109
    • Narcowich, F.J.1    Ward, J.D.2
  • 17
    • 0036433867 scopus 로고    scopus 로고
    • Scattered data interpolation on spheres: Error estimates and locally supported basis functions
    • F. J. NARCOWICH AND J. D. WARD, Scattered data interpolation on spheres: Error estimates and locally supported basis functions, SIAM J. Math. Anal., 33 (2002), pp. 1393-1410.
    • (2002) SIAM J. Math. Anal. , vol.33 , pp. 1393-1410
    • Narcowich, F.J.1    Ward, J.D.2
  • 19
    • 0030503790 scopus 로고    scopus 로고
    • Approximation by radial basis functions with finitely many centers
    • R. SCHABACK, Approximation by radial basis functions with finitely many centers, Constr. Approx., 12 (1996), pp. 331-340.
    • (1996) Constr. Approx. , vol.12 , pp. 331-340
    • Schaback, R.1
  • 20
    • 0033475852 scopus 로고    scopus 로고
    • Improved error bounds for scattered data interpolation by radial basis functions
    • R. SCHABACK, Improved error bounds for scattered data interpolation by radial basis functions, Math. Comp., 68 (1999), pp. 201-216.
    • (1999) Math. Comp. , vol.68 , pp. 201-216
    • Schaback, R.1
  • 21
    • 0346847275 scopus 로고
    • Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree
    • H. WENDLAND, Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree, Adv. Comput. Math., 4 (1995), pp. 389-396.
    • (1995) Adv. Comput. Math. , vol.4 , pp. 389-396
    • Wendland, H.1
  • 22
    • 0000764217 scopus 로고    scopus 로고
    • Error estimates for interpolation by compactly supported radial basis functions of minimal degree
    • H. WENDLAND, Error estimates for interpolation by compactly supported radial basis functions of minimal degree, J. Approx. Theory, 93 (1998), pp. 258-272.
    • (1998) J. Approx. Theory , vol.93 , pp. 258-272
    • Wendland, H.1
  • 24
    • 14544290310 scopus 로고
    • Local error estimates for radial basis function interpolation of scattered data
    • Z. WU AND R. SCHABACK, Local error estimates for radial basis function interpolation of scattered data, IMA J. Numer. Anal., 13 (1993), pp. 13-27.
    • (1993) IMA J. Numer. Anal. , vol.13 , pp. 13-27
    • Wu, Z.1    Schaback, R.2
  • 25
    • 0035556014 scopus 로고    scopus 로고
    • Spectral approximation orders of radial basis function interpolation on the Sobolev space
    • J. YOON, Spectral approximation orders of radial basis function interpolation on the Sobolev space, SIAM J. Math. Anal., 33 (2001), pp. 946-958.
    • (2001) SIAM J. Math. Anal. , vol.33 , pp. 946-958
    • Yoon, J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.