Details
| Original language | English |
|---|---|
| Pages (from-to) | 95-123 |
| Number of pages | 29 |
| Journal | Annales Mathematicae et Informaticae |
| Volume | 32 |
| Publication status | Published - 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.
Keywords
- De-Boor algorithm, ECT-B-splines, ECT-spline curves, ECT-systems
ASJC Scopus subject areas
- Computer Science(all)
- General Computer Science
- Mathematics(all)
- General Mathematics
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In: Annales Mathematicae et Informaticae, Vol. 32, 2005, p. 95-123.
Research output: Contribution to journal › Article › Research › 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 -