Error estimates and convergence rates for variational hermite interpolation

Journal of Approximation Theory

Volumn 95, Issue 2, 1998, Pages 264-279

  Luo, Zuhua ^a   Levesley, Jeremy ^a  

^a UNIVERSITY OF LEICESTER   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0008528922     PISSN: 00219045     EISSN: None     Source Type: Journal    
DOI: 10.1006/jath.1997.3218     Document Type: Article

References (18)

1. M. Atteia, "Hilbertian Kernels: Spline Functions," Studies in Computational Mathematics IV, North-Holland, Amsterdam, 1994.
2. A. Yu. Bezhaev and V. A. Vasilenko, "Variational Spline Theory," Bull. Novosibirsk Comput. Center, Special Issue No. 3 (1993).
3. W. F. Donoghue, "Distributions and Fouriertransforms," Academic Press, New York, 1969.
4. J. Duchon, Splines minimising rotation-invariant semi-norms in the Sobolev spaces, in "Constructive Theory of Functions of Several Variables" (W. Schempp and K. Zeller, Eds.), Lecture Notes in Mathematics, Vol. 571, pp. 85-100, Springer-Verlag, Berlin, 1977.
5. m-splines, RAIRO Anal. Numer. 12 (1978), 325-334.
6. M. Golomb and H. F. Weinberger, Optimal approximations and error bounds, in "On Numerical Approximations" (R. E. Langer, Ed.), pp. 117-190, Univ. of Wisconsin Press, Madison, 1959.
7. K. Jetter, S. D. Riemenschneider, and Z. Shen, Hermite interpolation on the lattice grid, SIAM J. Math. Anal. 25 (1994), 962-975.
8. P.-J. Laurent, "Approximation et Optimasation," Hermann, Paris, 1972.
9. Z. Luo and J. Levesley, "Error Estimates and Convergence Rates for Variational Hermite Interpolation," Research Report 1997/6, Department of Mathematics and Computer Science, University of Leicester, Leicester LEI 7RH, UK.
10. W. Light and H. Wayne, Error estimates for approximation by radial basis functions, in "Approximation Theory, Wavelets and Applications" (S. P. Singh, Ed.), pp. 215-246, Kluwer Academic, Dordrecht/Norwell, MA, 1994.
11. W. R. Madych and S. A. Nelson, Multivariate interpolation and conditionally positive definite functions, Approx. Theory Appl. 4 (1988), 77-89.
12. W. R. Madych and S. A. Nelson, Multivariate interpolation and conditionally positive definite functions, II, Math. Comp. 54 (1990), 211-230.
13. J. Meinguet, Multivariate interpolation at arbitrary points made simple, Z. Angew. Math. Phys. 30 (1979), 292-304.
14. F. J. Narcowich and J. D. Ward, Generalized Hermite interpolation via matrix-valued conditionally positive definite functions, Math. Comp. (1995).
15. M. J. D. Powell, "The Uniform Convergence of Thin Plate Spline Interpolation in Two Dimensions," Report No. DAMTP 1993/NA16, University of Cambridge, 1993.
16. Xingping Sun, Scattered Hermite interpolation using radial basis functions, Linear Algebra Appl. 207 (1994), 135-146.
17. Z. Wu, Hermite - Birkhoff interpolation of scattered data by radial basis functions, Approx. Theory Appl. 8 (1992), 1-10.
18. Z. Wu and R. Schabach, Local error estimates for radial basis function interpolation of scattered data, IMA J. Numer. Anal. 13 (1993), 13-27.