Abstract
We give necessary and sufficient conditions for the total positivity of certain connection matrices arising in piecewise exponential spline spaces. These total positivity conditions are sufficient for existence of B-splines in such spaces, but they are far from being necessary. We give a necessary and sufficient condition for existence of B-splines in the case of piecewise exponential spline spaces with only two differential operators, which eventually leads to a necessary condition for any piecewise exponential spline spaces.
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Communicated by M. Gasca
Dedicated to Professor Charles A. Micchelli for his 60th birthday
Mathematics subject classifications (2000)
65D17, 65D07, 41A15, 41A50.
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Lyche, T., Mazure, ML. Total positivity and the existence of piecewise exponential B-splines. Adv Comput Math 25, 105–133 (2006). https://doi.org/10.1007/s10444-004-7633-0
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DOI: https://doi.org/10.1007/s10444-004-7633-0