Abstract
Cardinal ECT-spline curves are generated from one ECT-system of order n which is shifted by integer translations via one connection matrix. If this matrix is nonsingular, lower triangular and totally positive, there exists an ECT-B-spline function N n0 (x) having minimal compact support [0,n] whose integer translates span the cardinal ECT-spline space. This B-spline is computed explicitly piece by piece. Involved is the characteristic polynomial of a certain matrix which is the product of a matrix related to the connection matrix and of the generalized Taylor matrix of the basic ECT-system. This approach extends results for polynomial cardinal splines via connection matrices [6] to the more general setting of cardinal ECT-splines. The method is illustrated by two examples based on ECT-systems of rational functions with prescribed poles. Also, a Green’s function involved is expressed explicitly as an ECT-B-splines series.
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Communicated by C. Brezinski
AMS subject classification
41A15, 41A05
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Tang, Y., Mühlbach, G.W. Cardinal ECT-splines. Numer Algor 38, 259–283 (2005). https://doi.org/10.1007/s11075-004-5301-6
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DOI: https://doi.org/10.1007/s11075-004-5301-6