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Volumn 15, Issue 2, 1999, Pages 175-208

Variational principles and Sobolev-type estimates for generalized interpolation on a Riemannian manifold

Author keywords

Approximation order; Positive definite kernels; Riemannian manifolds; Soholev spaces

Indexed keywords


EID: 0033239782     PISSN: 01764276     EISSN: None     Source Type: Journal    
DOI: 10.1007/s003659900104     Document Type: Article
Times cited : (51)

References (32)
  • 2
    • 0009211270 scopus 로고
    • A generalization of a multidimensional theorem of Bochner
    • Yu. M. BEREZANSKII (1961): A generalization of a multidimensional theorem of Bochner (English). Soviet Math., 2:143-147.
    • (1961) Soviet Math. , vol.2 , pp. 143-147
    • Berezanskii, Yu.M.1
  • 4
    • 0000273884 scopus 로고
    • Computing fourier transforms and convolutions for the 2-sphere
    • J. R. DRISCOLL, D. M. HEALY (1994): Computing fourier transforms and convolutions for the 2-sphere. Adv. in Appl. Math., 15:202-250.
    • (1994) Adv. in Appl. Math. , vol.15 , pp. 202-250
    • Driscoll, J.R.1    Healy, D.M.2
  • 5
    • 0017216638 scopus 로고
    • Interpolation des fonctions de deux variables suivant le principe de la flexion des plaques minces
    • J. DUCHON (1976): Interpolation des fonctions de deux variables suivant le principe de la flexion des plaques minces. RAIRO Anal. Numér., 10:5-12.
    • (1976) Rairo Anal. Numér. , vol.10 , pp. 5-12
    • Duchon, J.1
  • 6
    • 0001935440 scopus 로고
    • Splines minimizing rotation invariant semi-norms in Sobolev spaces
    • Oberwolfach 1976 (W. Schempp and K. Zeller, eds.). Berlin: Springer-Verlag
    • J. DUCHON (1977): Splines minimizing rotation invariant semi-norms in Sobolev spaces. In: Constructive Theory of Functions of Several Variables. Oberwolfach 1976 (W. Schempp and K. Zeller, eds.). Berlin: Springer-Verlag, pp. 85-100.
    • (1977) Constructive Theory of Functions of Several Variables , pp. 85-100
    • Duchon, J.1
  • 7
    • 0019712378 scopus 로고
    • On spherical spline interpolation and approximation
    • W. FREEDEN (1981): On spherical spline interpolation and approximation. Math. Methods Appl. Sci., 3:551-575.
    • (1981) Math. Methods Appl. Sci. , vol.3 , pp. 551-575
    • Freeden, W.1
  • 10
    • 0003037370 scopus 로고
    • Optimal approximation and error bounds
    • R. E. Langer, ed.. Madison
    • M. GOLOMB, H. F. WEINBERG (1959): Optimal approximation and error bounds. In: On Numerical Approximation (R. E. Langer, ed.). Madison, pp. 117-190.
    • (1959) On Numerical Approximation , pp. 117-190
    • Golomb, M.1    Weinberg, H.F.2
  • 12
    • 0002610173 scopus 로고
    • On a general method for decomposing positive-definite kernels into elementary products
    • M. G. KREIN (1946): On a general method for decomposing positive-definite kernels into elementary products (in Russian). Dokl. Akad. Nauk SSSR, 53:3-6.
    • (1946) Dokl. Akad. Nauk SSSR , vol.53 , pp. 3-6
    • Krein, M.G.1
  • 15
    • 0002642902 scopus 로고
    • Multivariate interpolation and conditionally positive definite functions
    • W. R. MADYCH, S. A. NELSON (1988): Multivariate interpolation and conditionally positive definite functions. Approx. Theory Appl., 4:77-79.
    • (1988) Approx. Theory Appl. , vol.4 , pp. 77-79
    • Madych, W.R.1    Nelson, S.A.2
  • 16
    • 84966244353 scopus 로고
    • Multivariate interpolation and conditionally positive definite functions II
    • W. R. MADYCH, S. A. NELSON (1990): Multivariate interpolation and conditionally positive definite functions II. Math. Comp., 54: 211-230.
    • (1990) Math. Comp. , vol.54 , pp. 211-230
    • Madych, W.R.1    Nelson, S.A.2
  • 17
    • 84942971733 scopus 로고    scopus 로고
    • Strictly positive definite kernels on the Hilbert sphere
    • to appear
    • V. A. MENEGATTO (to appear): Strictly positive definite kernels on the Hilbert sphere. Appl. Anal.
    • Appl. Anal.
    • Menegatto, V.A.1
  • 19
    • 0001134183 scopus 로고
    • Generalized hermite interpolation and positive definite kernels on a Riemannian manifold
    • F. J. NARCOWICH (1995): Generalized Hermite interpolation and positive definite kernels on a Riemannian manifold. J. Math. Anal. Appl., 190:165-193.
    • (1995) J. Math. Anal. Appl. , vol.190 , pp. 165-193
    • Narcowich, F.J.1
  • 20
    • 84968510026 scopus 로고
    • Generalized Hermite interpolation via matrix-valued conditionally positive definite kernels
    • F. J. NARCOWICH, J. D. WARD (1994): Generalized Hermite interpolation via matrix-valued conditionally positive definite kernels. Math. Comp., 63:661-688.
    • (1994) Math. Comp. , vol.63 , pp. 661-688
    • Narcowich, F.J.1    Ward, J.D.2
  • 21
    • 0001739142 scopus 로고
    • The theory of radial basis approximation in 1990
    • W. Light, ed.. Oxford, UK: Oxford University Press
    • M. J. D. POWELL (1990): The theory of radial basis approximation in 1990. In: Wavelets, Subdivision and Radial Functions (W. Light, ed.). Oxford, UK: Oxford University Press.
    • (1990) Wavelets, Subdivision and Radial Functions
    • Powell, M.J.D.1
  • 22
    • 0030487411 scopus 로고    scopus 로고
    • Strictly positive definite functions on spheres
    • A. RON, X. SUN (1996): Strictly positive definite functions on spheres. Math. Comp., 65:1513-1530.
    • (1996) Math. Comp. , vol.65 , pp. 1513-1530
    • Ron, A.1    Sun, X.2
  • 23
    • 51249166702 scopus 로고
    • Error estimates and condition numbers for radial basis function interpolation
    • R. SCHABACK (1995): Error estimates and condition numbers for radial basis function interpolation. Adv. in Comput. Math., 3:251-264.
    • (1995) Adv. in Comput. Math. , vol.3 , pp. 251-264
    • Schaback, R.1
  • 24
    • 0001878701 scopus 로고
    • Positive definite functions on spheres
    • I. J. SCHOENBERG (1942): Positive definite functions on spheres. Duke Math. J., 9:96-108.
    • (1942) Duke Math. J. , vol.9 , pp. 96-108
    • Schoenberg, I.J.1
  • 25
    • 0001558197 scopus 로고
    • Positive definite functions and generalizations, an historical survey
    • J. STEWART (1976): Positive definite functions and generalizations, an historical survey. Rocky Mountain J. Math., 6:409-434.
    • (1976) Rocky Mountain J. Math. , vol.6 , pp. 409-434
    • Stewart, J.1
  • 26
    • 0002928486 scopus 로고
    • Spline interpolation and smoothing on the sphere
    • G. WAHBA (1981): Spline interpolation and smoothing on the sphere. SIAM J. Sci. Statist. Comput., 2:5-16.
    • (1981) Siam J. Sci. Statist. Comput. , vol.2 , pp. 5-16
    • Wahba, G.1
  • 27
    • 0001388356 scopus 로고
    • Surface fitting with scattered noisy data on Euclidean d-space and on the sphere
    • G. WAHBA (1984): Surface fitting with scattered noisy data on Euclidean d-space and on the sphere. Rocky Mountain J. Math., 14:281-299.
    • (1984) Rocky Mountain J. Math. , vol.14 , pp. 281-299
    • Wahba, G.1
  • 29
    • 0002479849 scopus 로고
    • Hermite-Birkhoff interpolation of scattered data by radial basis functions
    • Z. WU (1992): Hermite-Birkhoff interpolation of scattered data by radial basis functions. Approx. Theory Appl., 24:201-215.
    • (1992) Approx. Theory Appl. , vol.24 , pp. 201-215
    • Wu, Z.1
  • 30
    • 14544290310 scopus 로고
    • Local error estimates for radial basis function interpolation of scattered data
    • Z. WU, R. SCHABACK (1993): Local error estimates for radial basis function interpolation of scattered data. IMA J. Numer. Anal., 13:13-27.
    • (1993) IMA J. Numer. Anal. , vol.13 , pp. 13-27
    • Wu, Z.1    Schaback, R.2
  • 31
    • 84966231566 scopus 로고
    • Strictly positive definite functions on spheres
    • Y. XU, E. W. CHENEY (1992): Strictly positive definite functions on spheres. Proc. Amer. Math. Soc., 116:977-981.
    • (1992) Proc. Amer. Math. Soc. , vol.116 , pp. 977-981
    • Xu, Y.1    Cheney, E.W.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.