Mühlbach, Günter W., Tang, Yuehong (2005) Construction of ECT-B-splines, a survey Annales Mathematicae et Informaticae. 32. pp. 95-123. ISSN 1787-6117
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Absztrakt (kivonat)
s-dimensional generalized polynomials are linear combinations of functions forming an ECT-system on a compact interval with coefficients from R . ECT-spline curves in R are constructed by glueing together at interval endpoints generalized polynomials generated from different local ECT-systems via connection matrices. If they are nonsingular, lower triangular and totally positive there is a basis of the space of 1-dimensional ECT-splines consisting of functions having minimal compact supports normalized to form a nonnegative partition of unity. Its functions are called ECT-B-splines. One way (which is semiconstructional) to prove existence of such a basis is based upon zero bounds for ECT-splines. A constructional proof is based upon a definition of ECT-B-splines by generalized divided differences extending Schoenberg’s classical construction of ordinary polynomial B-splines. This fact eplains why ECT-B-splines share many properties with ordinary polynomial B-splines. In this paper we survey such constructional aspects of ECT-splines which in particular situations reduce to classical results. s Key Words: ECT-systems, ECT-B-splines, ECT-spline curves, de-Boor algorithm AMS Classification Number: 41A15, 41A05
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Nyelv: | angol | ||||||||||||
Kötetszám: | 32. | ||||||||||||
ISSN: | 1787-6117 | ||||||||||||
Felhasználó: | Tibor Gál | ||||||||||||
Dátum: | 10 Feb 2019 15:39 | ||||||||||||
Utolsó módosítás: | 10 Feb 2019 15:39 | ||||||||||||
URI: | http://publikacio.uni-eszterhazy.hu/id/eprint/2642 |
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