Geodesic
On a new family of conditionally positive definite radial basis functions
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 19 (2013) no. 2, pp. 256-266 Cet article a éte moissonné depuis la source Math-Net.Ru

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A new family of conditionally positive definite radial basis functions is proposed, which can be applied for constructing multivariate splines in $\mathbb R^d$, $d\in\mathbb N$. The family is a natural generalization of known constructions of splines with tension and regularized splines.
Keywords: completely monotonic function, radial basis function, spline. 
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A. I. Rozhenko. On a new family of conditionally positive definite radial basis functions. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 19 (2013) no. 2, pp. 256-266. http://geodesic.mathdoc.fr/item/TIMM_2013_19_2_a24/

[1] Duchon J., “Spline minimizing rotation-invariant seminorms in Sobolev spaces”, Lect. Notes Math., 571, Springer, Berlin, 1977, 85–100 | DOI | MR

[2] Mitáš L., Mitášová H., “General variational approach to the interpolation problem”, Comput. Math. Appl., 16:12 (1988), 983–992 | DOI | MR | Zbl

[3] Matérn B., Spatial variation, Lect. Notes in Statistics, 36, 2nd ed., Springer-Verlag, Berlin, 1986, 151 pp. | MR | Zbl

[4] M. Abramovits, I. Stigan (red.), Spravochnik po spetsialnym funktsiyam s formulami, grafikami i matematicheskimi tablitsami, per. s angl., red. per. V. A. Ditkin, L. N. Karmazina, Nauka, M., 1979, 832 pp. | MR

[5] Schaback R., Wendland H., “Characterization and construction of radial basis functions”, Multivariate approximation and applications, eds. N. Dyn, D. Leviatan, D. Levin, A. Pinkus, Cambridge University Press, Cambridge, 2001, 1–24 | DOI | MR | Zbl

[6] Micchelli C. A., “Interpolation of scattered data: Distance matrices and conditionally positive definite functions”, Constr. Approx., 2:1 (1986), 11–22 | DOI | MR | Zbl

[7] Volkov Yu. S., Miroshnichenko V. L., “Postroenie matematicheskoi modeli universalnoi kharakteristiki radialno-osevoi gidroturbiny”, Sib. zhurn. industr. matematiki, 1:1 (1998), 77–88 | Zbl

[8] Powell M. J. D., “The theory of radial basis function approximation in 1990”, Advances in numerical analysis, v. II, Wavelets, subdivision algorithms and radial basis functions, ed. W. A. Light, Oxford Univ. Press, Oxford, 1992, 105–210 | MR

[9] Beitmen G., Erdeii A., Vysshie transtsendentnye funktsii, per. s angl., red. per. N. Ya. Vilenkin, v. 2, Funktsii Besselya, funktsii parabolicheskogo tsilindra, ortogonalnye mnogochleny, eds. L. A. Lyusternik, A. R. Yanpolskii, Nauka, M., 1966, 297 pp. | MR

[10] Schaback R., Wendland H., “Inverse and saturation theorems for radial basis function interpolation”, Math. Comp., 71:238 (2002), 669–681 | DOI | MR | Zbl

[11] Madych W. R., Nelson S. A., “Multivariate interpolation and conditionally positive definite functions. II”, Math. Comp., 54:189 (1990), 211–230 | DOI | MR | Zbl