Geodesic
Multidimensional Iterative Interpolation
Canadian journal of mathematics, Tome 43 (1991) no. 2, pp. 297-312

Voir la notice de l'article provenant de la source Cambridge University Press

We define an iterative interpolation process for data spread over a closed discrete subgroup of the Euclidean space. We describe the main algebraic properties of this process. This interpolation process, under very weak assumptions, is always convergent in the sense of Schwartz distributions. We find also a convenient necessary and sufficient condition for continuity of each interpolation function of a given iterative interpolation process.
DOI : 10.4153/CJM-1991-016-4
Mots-clés : Iterative interpolation process, fundamental interpolating function, characteristic function, continuous interpolation, temperate distribution, Fourier transform, 65D05, 65D10, 26B05, 65Q05, 42A05, 42A38 
Deslauriers, Gilles; Dubois, Jacques; Dubuc, Serge. Multidimensional Iterative Interpolation. Canadian journal of mathematics, Tome 43 (1991) no. 2, pp. 297-312. doi: 10.4153/CJM-1991-016-4
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[1] 1. Daubechies, I. and Lagarias, J., Two-scale Difference Equations I Global Regularity of Solutions & II Local Regularity, Infinite Products of Matrices and Fractals, SIAM J. Math. Anal., (to appear). Google Scholar

[2] 2. Deslauriers, G., Dubuc, S., Interpolation dyadique.ln Fractals: Dimensions non entières et applications, Masson Paris, 1987, 44–55. Google Scholar

[3] 3. Deslauriers, G., Dubuc, S., Transformées de Fourier de courbes irrégulières, (Comptes Rendus de l'atelier de géométrie fractale. Mai 1986.) Ann. se. math. Québec. (1)11(1987), 25–44. Google Scholar

[4] 4. Deslauriers, G., Dubuc, S., Symmetric Iterative Interpolation Processes, Constructive Approximation 5(1989), 49–68. Google Scholar

[5] 5. Dubuc, S., Interpolation through an Iterative Scheme, J. of Math. Anal, and Appl.,( 1)114(1986), 185–204. Google Scholar

[6] 6. Dyn, N., Levin, D. and Gregory, J.A.,A 4-point interpolatory subdivision scheme for curve design, Computer Aided Geometric Design 4(1987), 257–268. Google Scholar

[7] 7. Dyn, N., Levin, D. and Gregory, J.A., Analysis of uniform binary subdivision schemes for curve design, Constructive Approximation, (to appear). Google Scholar

[8] 8. Falconer, K.J., The Hausdorff dimension of se If-affine fractals, Math. Proc. Cambridge Philos. Soc. 103(1988), 339–350. Google Scholar

[9] 9. Henrici, P., Elements of Numerical Analysis. John Wiley & Sons Inc.,New York, 1964. Google Scholar

[10] 10. Kôno, N., On self-affine functions, Japan J. Appl. Math. 3(1986), 259–269. Google Scholar

[11] 11. Mandelbrot, B.B., The Fractal Geometry of Nature. W.H. Freeman, San Francisco, 1982. Google Scholar

[12] 12. Micchelli, C.A. and Prautzsch, H., Computing surfaces invariant under subdivision, Computer Aided Geometric Design 4(1987), 321–328. Google Scholar

[13] 13. Micchelli, C.A. and Prautzsch, H., Uniform refinement of curves, Linear Algebra and Applications, 114/115(1989), 841–870. Google Scholar

[14] 14. Smith, G.B., A Fast Surface Interpolation Technique, in Proc. DARPA, Image Understanding Workshop, Oct. 1984,211–215. Google Scholar

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