Distance Matrices and Ridge Function Interpolation
Canadian journal of mathematics, Tome 45 (1993) no. 6, pp. 1313-1323

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A geometric characterization is given for a collection of points in Rd to produce a singular l1 -distance matrix. Some quantitative results are established in terms of "characteristic matrices". The results in this paper generalize those of Dyn, Light and Cheney and have application to ridge function interpolation.
DOI : 10.4153/CJM-1993-074-9
Mots-clés : 41A05, 41A63
Reid, Les; Sun, Xingping. Distance Matrices and Ridge Function Interpolation. Canadian journal of mathematics, Tome 45 (1993) no. 6, pp. 1313-1323. doi: 10.4153/CJM-1993-074-9
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[B] Bellman, R., Introduction to Matrix Analysis, McGraw-Hill Book Company, 1960. Google Scholar

[BP] Braess, D. and Pinkus, A., Interpolation by ridge functions , J. Approx. Theory, to appear. Google Scholar

[DS] Diliberto, S. P. and Straus, E.G., On the approximation of a function of several variable by the sum of functions of fewer variables, Pacific J. Math. 1(1951), 195–210. Google Scholar

[DLC] Dyn, N., Light, W.A. and Cheney, E.W., Interpolation by piecewise-linear radial basis functions I, J. Approx. Theory 59(1989), 202–223. Google Scholar

[H] Herz, C.S., Une ébauche d'une théorie générale des fonctions définie s-négative , Séminaire Brelot- Choquet-Deny (Théorie du Potentiel), 7eannée, Inst. Henri Poincaré, Paris. Google Scholar

[L] Light, W.A., The singularity of distance matrices. In: Multivariate Approximation Theory, (eds. Schempp, W., Chui, C. and Zeller, K.), Birkhauser-Verlag (1989), 233–240. Google Scholar

[SI] Schoenberg, I.J., On certain metric spaces arising from Euclidean spaces by a change of metric and their imbedding in Hilbert space, Ann. Math. 38(1937), 787–793. Google Scholar

[S2] Schoenberg, I.J., Metric spaces and positive definite functions, Trans. Amer. Math. Soc. 44(1938), 522–536. Google Scholar

[S3] Schoenberg, I.J., Metric spaces and completely monotone functions, Ann. Math. 39(1938), 811–841. Google Scholar

[SX] Sun, X., Multivariate interpolation by a general class of functions , J. Approx. Theory, to appear. Google Scholar

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