Spaces of distributions, interpolation by translates of a basis function and error estimates

Numerische Mathematik

Volumn 81, Issue 3, 1999, Pages 415-450

  Light, Will ^a   Wayne, Henry ^a  

^a UNIVERSITY OF LEICESTER   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033477931     PISSN: 0029599X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002110050398     Document Type: Article

References (19)

1. Deny, J., Lions, J.L. (1954): Les espaces du type de Beppo Levi, Ann. Inst. Fourier 5, 305-370
2. m-splines, RAIRO Analyse Numerique 12 (4), 325-334
3. Duchon, J. (1977): Splines minimising rotation-invariant seminorms in Sobolev spaces, in Constructive theory of functions of several variables, Lecture Notes in Mathematics, 571, Schempp, W., Zeller, K. (eds.) Springer-Verlag (Berlin), 85-100
4. Golomb, M., Weinberger, H.F. (1959): Optimal approximation and error bounds, in On numerical approximation, ed. Langer, R.E., University of Wisconsin Press (Madison), 117-190
5. Gelfand, I.M., Vilenkin, N.Ya. (1964): Generalised functions, Vol 4, Academic Press, New York
6. Hadamard, J. (1923): Lectures on Cauchy's problem in linear partial differential equations, Yale University Press, New Haven, Conn.
7. Hörmander, L. (1958): On the division of distributions by polynomials, Arkiv för Mat. 53 (3), 555-568
8. Hörmander, L. (1983): The analysis of linear partial differential operators I, Springer Verlag, Berlin
9. Light, W.A., Wayne, H.S.J. (1995): Some aspects of radial basis function approximation, in Approximation theory, spline functions and applications, ed. Singh, S.P., Kluwer Academic Publishers, Dordrecht, 163-190
10. Light, W.A., Wayne, H.S.J. (1998): On power functions and error estimates for radial basis function interpolation, J. Approx. Th. 92, 245-266
11. Madych, W., Nelson, S. (1988): Multivariate interpolation and conditionally positive definite functions, Approx. Theory Appl. 4, 77-89
12. Madych, W.R., Nelson, S.A. (1990): Multivariate interpolation and conditionally positive definite functions II, Math. Comp. 54, 211-230
13. Micchelli, C.A. (1986): Interpolation of scattered data: distance matrices and conditionally positive definite functions, Constr. Approx. 2, 11-22
14. Rudin, W. (1973): Functional analysis, McGraw-Hill, New York
15. Schaback, R. (1995): Multivariate interpolation and approximation by translates of a basis function, in Approximation Theory VIII, VoI I: Approximation and interpolation, Chui, C.K., Larry L. Schumaker (eds.) World Scientific Publishing Co., Singapore, 491-514
16. Schoenberg, I.J. (1938): Metric spaces and completely monotone functions, Annals of Math., 39, 811-841
17. Schwartz, L. (1966): Théorie des distributions, Hermann, Paris
18. Stein, E.M., Weiss, G. (1971): Fourier analysis on Euclidean spaces, Princeton University Press, Princeton
19. Wu, Zong-Min, Schaback, R. (1993): Local error estimates for radial basis function interpolation to scattered data, IMA J. Numer. Anal. 13, 13-27