## Quasi-Chebyshev splines with connection matrices: Application to variable degree polynomial splines.(English)Zbl 0978.41006

Extending a result recently obtained for Chebyshev splines, we give a necessary and sufficient condition for the existence of blossoms (or, equivalently, of $$B$$-spline bases) for splines with connection matrices and with sections in different four-dimensional quasi-Chebyshev spaces. We apply this result to the study of variable degree polynomial splines.

### MSC:

 41A15 Spline approximation
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### References:

 [1] Costantini, P., Shape preserving interpolation with variable degree polynomial splines, (), 87-114 · Zbl 0867.68107 [2] Costantini, P., Variable degree polynomial splines, (), 85-94 · Zbl 0938.65018 [3] Costantini, P., Curve and surface construction using variable degree polynomial splines, Computer aided geometric design, 17, 419-446, (2000) · Zbl 0938.68128 [4] Goodman, T.N.T., Mazure, M.-L., 1999. Blossoming beyond extended Chebyshev spaces, RR 1018M IMAG, Université Joseph Fourier, J. Approx. Theory, to appear [5] Kaklis, P.D.; Pandelis, D.G., Convexity preserving polynomial splines of non-uniform degree, IMA J. numer. anal., 10, 223-234, (1990) · Zbl 0699.65007 [6] Kaklis, P.D.; Sapidis, N.S., Convexity preserving interpolatory parametric splines of non-uniform polynomial degree, Computer aided geometric design, 12, 1-26, (1995) · Zbl 0875.68831 [7] Mazure, M.-L., Blossoming of Chebyshev splines, (), 355-364 · Zbl 0835.65033 [8] Mazure, M.-L., Blossoming: A geometrical approach, Constr. approx., 15, 33-68, (1999) · Zbl 0924.65010 [9] Mazure, M.-L., 2000. Chebyshev splines beyond total positivity, RR 1027M IMAG, Université Joseph Fourier (Advances in Computat. Math., to appear) [10] Mazure, M.-L.; Pottmann, H., Tchebycheff curves, (), 187-218 · Zbl 0902.41018 [11] Pottmann, H., The geometry of Tchebycheffian splines, Computer aided geometric design, 10, 181-210, (1993) · Zbl 0777.41016
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