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On dimension elevation in quasi extended Chebyshev spaces. (English) Zbl 1144.65013

The present paper is motivated by one of the results on a dimension elevation process involving numbers \(p, q\) and a chosen integer \(n\) with \(p=q \geq 3\) and \(2 \leq n \leq p-1 \), proved by P. Costantini, T. Lyche and C. Manni [Numer. Math. 101, No. 2, 333–354 (2005; Zbl 1085.41002)]. Via blossoms, the author shows that the foregoing result can be extended to the case when \(p, q \) are greater than \(2\) and \(2 \leq n\leq \operatorname{Min}(p,q)\). A similar study of quasi-extended Chebyshev spaces is also made.

MSC:

65D18 Numerical aspects of computer graphics, image analysis, and computational geometry

Citations:

Zbl 1085.41002
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References:

[1] Costantini, P.: On monotone and convex spline interpolation. Math. Comp. 46, 203–214 (1986) · Zbl 0617.41015
[2] Costantini, P.: Shape preserving interpolationwith variable degree polynomial splines. In: Hoscheck, J., Kaklis, P. (eds.) Advanced Course on FAIRSHAPE, pp. 87–114. B.G. Teubner, Stuttgart (1996) · Zbl 0867.68107
[3] Costantini, P.: Variable degree polynomial splines. In: Le Méhauté, A., Rabut, C., Schumaker, L.L. (eds.) Curves and Surfaces with Applications in CAGD, pp. 85–94. Vanderbilt University Press, Nashvile (1997) · Zbl 0938.65018
[4] Costantini, P., Lyche, T., Manni, C.: On a class of weak Tchebycheff systems. Numer. Math. 101, 333–354 (2005) · Zbl 1085.41002
[5] Goodman, T.N.T., Mazure, M.-L.: Blossoming beyond extended Chebyshev spaces. J. Approx. Theory 109, 48–81 (2001) · Zbl 0996.41005
[6] Mazure, M.-L., Laurent, P.-J.: Nested sequences of Chebyshev spaces. Math. Model. Numer. Anal. 32, 773–788 (1998) · Zbl 0922.65010
[7] Mazure, M.-L.: Ready-to-blossom bases in Chebyshev spaces. In: Jetter, K., Buhmann, M., Haussmann, W., Schaback, R., et Stoeckler, J. (eds.) Topics in Multivariate Approximation and Interpolation., vol. 12, pp. 109–148. Elsevier, Amsterdam (2006)
[8] Mazure, M.-L.: Which spaces for design. preprint
[9] Mazure, M.-L., Pottmann, H.: Tchebycheff curves. In: Total Positivity and its Applications, pp. 187–218. Kluwer, Dordrecht (1996) · Zbl 0902.41018
[10] Pottmann, H.: The geometry of Tchebycheffian splines. Comp. Aided Geometric Des. 10, 181–210 (1993) · Zbl 0777.41016
[11] Ramshaw, L.: Blossoms are polar forms. Comp. Aided Geometric Des. 6, 323–358 (1989) · Zbl 0705.65008
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