Recurrence relations for Tchebycheffian B-splines |
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Authors: | Nira Dyn Amos Ron |
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Affiliation: | (1) School of Mathematical Sciences, Tel Aviv University, Tel Aviv, Israel |
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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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