Interpolation by basis functions of different scales and shapes

Calcolo

Volumn 41, Issue 2, 2004, Pages 77-87

  Bozzini, M ^a   Lenarduzzi, L ^b   Rossini, M ^a   Schaback, R ^c  

^a UNIVERSITY OF MILANO BICOCCA   (Italy)

^b CNR   (Italy)

^c UNIVERSITY OF GÖTTINGEN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

FUNCTIONS; MATRIX ALGEBRA; PERTURBATION TECHNIQUES; RADIAL BASIS FUNCTION NETWORKS;

BASE FUNCTION; DATA DENSITY; INTERPOLATION MATRIX; LOCAL DATA; MULTIVARIATE DATA; POSITIVE DEFINITE; SCALE AND SHAPES; SCALINGS; SIGNAL BEHAVIOR; SYMMETRICS;

INTERPOLATION;

EID: 17444393519     PISSN: 00080624     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10092-004-0085-6     Document Type: Article

References (25)

1. Ball, K.: Eigenvalues of Euclidean distance matrices. J. Approx. Theory 68, 74-82 (1992)
2. Ball, K., Sivakumar, N., Ward, J.D.: On the sensitivity of radial basis interpolation to minimal data separation distance. Constr. Approx. 8, 401-426 (1992)
3. Baxter, B.J.C.: Norm estimates for inverses of Toeplitz distance matrices. J. Approx. Theory 79, 222-242 (1994)
4. Baxter, B.J.C., Sivakumar, N.: On shifted cardinal interpolation by Gaussians and multiquadrics. J. Approx. Theory 87, 36-59 (1996)
5. Dozziui, M., Lenarduzzi, L., Schaback, R.: Adaptive interpolaticn by scaled multiquadrics. Adv. Comput. Math. 16, 375-387 (2002)
6. Buhmann, M.D.: Radial basis functions. In: Iserless, A. (ed.): Acta numerica.(Acta Numerica 9) Cambridge: Cambridge Univ. Press 2000, pp. 1-37
7. Buhmann, M.D., Micchelli, C.A.: Multiquadric interpolation improved. Comput. Math. Appl. 24, 21-25 (1992)
8. 2 in multiquadric interpolation. Comput. Math. Appl. 21, 29-42 (1991)
9. Fasshauer, G.: On smoothing for multilevel approximation with radial basis functions, hi: Chui, C.K., Schumaker, L.L. (eds): Approximation theory IX. Vol. 2. Computational aspects. Nashville: Vanderbilt University Press 1998, pp. 55-62
10. Franke, R., Hagen, H., Nielson, G.M.: Least squares surface approximation to scattered data using multiquadratic functions. Adv. Comput. Math. 2, 81-99 (1994)
11. Galperin, E.A., Zheng, Q.: Solution and control of PDE via global optimization methods. Comput. Math. Appl. 25, 103-118 (1993)
12. Hagan, R.E., Kansa, E.J.: Studies of the R parameter in the multiquadric function applied to groundwater pumping. J. Appl. Sci. Comput. 1, 266-282 (1994)
13. Hon, Y.C., Kansa, E. J.: Circumventing the ill-conditioning problem with multiquadric radial basis functions: applications to elliptic partial differential equations. Comput. Math. Appl. 39, 123-127 (2000)
14. Horn, R.A., Johnson, C.R.: Matrix analysis. Cambridge: Cambridge University Press 1985
15. Kansa, E.J.: Multiquadrics - a scattered data approximation scheme with applications to computational fluid-dynamics. I. Surface approximation and partial dervative estimates. Comput. Math. Appl. 19, 127-145 (1990)
16. Madych, W.R.: Cardinal interpolation with polyharmonic splines. In: Schempp, W. et al. (eds.): Multivariate approximation theory. IV. Basel: Birkhäuser 1989, pp. 241-248
17. Narcowich, F.J., Sivakumar, N., Ward, J.D.: On condition numbers associated with radial-function interpolation. J. Math. Anak Appl. 186, 457-185 (1994)
18. Narcowich, F.J., Ward, J.D.: Norm estimates for the inverses of a general class of scattered-data radial-function interpolation matrices. J. Approx. Theory 69, 84-109 (1992)
19. Powell, M.J.D.: The theory of radial basis function approximation in 1990. In: Light, W.A. (ed.): Advances in numerical analysis. II. Wavelets, subdivision algorithms, and radial basis functions. Oxford: Oxford Univ. Press 1992, pp. 105-210
20. P and power-growth data. Adv. Comput. Math. 11, 229-251 (1999)
21. Schaback, R.: Lower bounds for norms of inverses of interpolation matrices for radial basis functions. J. Approx. Theory 79, 287-306 (1994)
22. Schaback, R.: Error estimates and condition numbers for radial basis function interpolation. Adv. Comput. Math. 3, 251-264 (1995)
23. Schaback, R., Wendland, H.: Characterization and construction of radial basis functions. In: Dyn, N., et al. (eds.): Multivariate approximation and applications. Cambridge: Cambridge University Press 2001, pp. 1-24
24. Wendland, H.: Konstruktion und Untersuchung radialer Basisfunktionen mit kompaktem Träger. Dissertation. Göttingen: Universität Göttingen 1996
25. Wendland, H., Narcowich, F.J., Ward, J.D.: Refined error estimates for radial basis function interpolation. Constr. Approx. 19, 541-564 (2003)