On the stationary Lp -approximation power to derivatives by radial basis function interpolation

Applied Mathematics and Computation

Volumn 150, Issue 3, 2004, Pages 875-887

  Yoon, Jungho ^a  

^a Ewha Womans University   (South Korea)

Author keywords

'Shifted' surface spline; Approximation power; Homogeneous Sobolev space; Interpolation; Multiquadric; Radial basis function

Indexed keywords

APPROXIMATION THEORY; FUNCTIONS; LINEAR SYSTEMS; PARTIAL DIFFERENTIAL EQUATIONS; THEOREM PROVING;

APPROXIMATION POWER; HOMOGENEOUS SOBOLEV SPACE; RADIAL BASIS FUNCTIONS;

INTERPOLATION;

EID: 1242298815     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2003.10.009     Document Type: Article

References (15)

1. Abramowitz M., Stegun I. A Handbook of Mathematical Functions. 1970;Dover, New York.
2. Baxter B.J.C., Sivakumar N., Ward J.D. Regarding the p-norms of radial basis interpolation matrices. Constr. Approx. 10:1994;451-468.
3. Buhmann M.D. New developments in the theory of radial basis function interpolation. Jetter K., Utreras F.I. Multivariate Approximation: From CAGD to Wavelets. 1993;35-75 World Scientific, Singapore.
4. Dyn N. Interpolation and approximation by radial and related functions. Chui C.K., Schumaker L.L., Ward J. Approximation Theory VI. 1989;211-234 Academic Press, New York.
5. m -splines RAIRO Analyse Numerique. 12:1978;325-334.
6. Folland G.B. Real Analysis. 1984;Wiley, New York.
7. Gelfand I.M., Shilov G.E. Generalized Functions. vol. 1:1964;Academic Press, New York.
8. Micchelli C.A. Interpolation of scattered data: distances, matrices, and conditionally positive functions. Constr. Approx. 2:1986;11-22.
9. Madych W.R., Nelson S.A. Multivariate interpolation and conditionally positive functions I. Approximation Theory and its Applications. 4(4):1988;77-89.
10. Madych W.R., Nelson S.A. Multivariate interpolation and conditionally positive functions II. Math. Comp. 54:1990;211-230.
11. Narcowich F.J., Ward J.D. Norms of inverses and condition numbers for matrices associated with scattered data. J. Approx. Theory. 64:1991;69-94.
12. Powell M.J.D. The theory of radial basis function approximation in 1990. Light W.A. Advances in Numerical Analysis vol. II: Wavelets, Subdivision Algorithms and Radial Basis Functions. 1992;105-210 Oxford University Press, Oxford.
13. Wu Z., Schaback R. Local error estimates for radial basis function interpolation of scattered data. IMA J. Numer. Anal. 13:1993;13-27.
14. d) from a space spanned by the scattered shifts of a radial basis function Constr. Approx. 17:2001;227-247.
15. p -Error estimates for 'shifted' surface spline interpolation on Sobolev space Math. Comp. 72:2003;243. 1349-1367.