Construction of ECT-B-splines, a survey

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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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

Mű típusa: Folyóiratcikk
Szerző:
Szerző neveMTMT azonosítóORCID azonosítóKözreműködés
Mühlbach, Günter W.NEM RÉSZLETEZETTNEM RÉSZLETEZETTSzerző
Tang, YuehongNEM RÉSZLETEZETTNEM RÉSZLETEZETTSzerző
Kapcsolódó URL-ek:
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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