Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 95-123 |
| Seitenumfang | 29 |
| Fachzeitschrift | Annales Mathematicae et Informaticae |
| Jahrgang | 32 |
| Publikationsstatus | Veröffentlicht - 2005 |
Abstract
s-dimensional generalized polynomials are linear combinations of functions forming an ECT-system on a compact interval with coefficients from Rs. ECT-spline curves in Rs are constructed by glueing together at interval end-points 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 non-negative 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.
ASJC Scopus Sachgebiete
- Informatik (insg.)
- Allgemeine Computerwissenschaft
- Mathematik (insg.)
- Allgemeine Mathematik
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in: Annales Mathematicae et Informaticae, Jahrgang 32, 2005, S. 95-123.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - Construction of ECT-B-splines, a survey
AU - Mühlbach, Günter W.
AU - Tang, Yuehong
PY - 2005
Y1 - 2005
N2 - s-dimensional generalized polynomials are linear combinations of functions forming an ECT-system on a compact interval with coefficients from Rs. ECT-spline curves in Rs are constructed by glueing together at interval end-points 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 non-negative 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.
AB - s-dimensional generalized polynomials are linear combinations of functions forming an ECT-system on a compact interval with coefficients from Rs. ECT-spline curves in Rs are constructed by glueing together at interval end-points 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 non-negative 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.
KW - De-Boor algorithm
KW - ECT-B-splines
KW - ECT-spline curves
KW - ECT-systems
UR - http://www.scopus.com/inward/record.url?scp=85042084887&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:85042084887
VL - 32
SP - 95
EP - 123
JO - Annales Mathematicae et Informaticae
JF - Annales Mathematicae et Informaticae
SN - 1787-5021
ER -