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Recurrence relations for Tchebycheffian B-splines

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Abstract

Four-term recurrence relations with constant coefficients are derived for a wide class of T chebycheffian B-splines, LB-splines and complex B-splines. Such a relation exists whenever the differential operator defining the underlying “polynomial” space can be factored in two essentially different ways. The four lower order B-splines in the recurrence relation appear in two pairs, each pair corresponding to one of these factorization. It is shown that the two-term recurrence relations for polynomial, trigonometric and hyperbolic B-splines as well as other known two-term recurrence relations are obtained directly from the four-term recurrence relations in a unified and systematic way. The above derivation also yields two different two-term recurrence relations for Green’s functions of these “polynomial” spaces In this context the special examples of exponential functions and rational functions are analyzed in detail.

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Authors and Affiliations

  1. School of Mathematical Sciences, Tel Aviv University, Tel Aviv, Israel

    Nira Dyn & Amos Ron

Authors
  1. Nira Dyn
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  2. Amos Ron
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Dyn, N., Ron, A. Recurrence relations for Tchebycheffian B-splines. J. Anal. Math. 51, 118–138 (1988). https://doi.org/10.1007/BF02791121

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  • DOI: https://doi.org/10.1007/BF02791121

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