Details
| Original language | English |
|---|---|
| Pages (from-to) | 96-122 |
| Number of pages | 27 |
| Journal | Journal of Computational and Applied Mathematics |
| Volume | 187 |
| Issue number | 1 |
| Early online date | 27 Apr 2005 |
| Publication status | Published - 1 Mar 2006 |
Abstract
ECT-spline curves are 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 ECT-splines consisting of functions having minimal compact supports, normalized either to form a nonnegative partition of unity or to have integral one. In this paper such ECT-B-splines are defined by generalized divided differences. This definition reduces to the classical one in case of a Schoenberg space. Under suitable assumptions it leads to a recursive method for computing the ECT-B-splines that reduces to the de Boor-Mansion-Cox recursion in case of ordinary polynomial splines and to Lyche's recursion in case of Tchebycheff splines [Mühlbach and Tang, Calculation of ECT-B-splines and of ECT-spline curves recursively, in preparation]. There is an ECT-spline space naturally adjoint to every ECT-spline space. We also construct B-splines via generalized divided differences for this space and study relations between the two adjoint spaces.
Keywords
- ECT-B-splines, ECT-systems, Generalized divided differences
ASJC Scopus subject areas
- Mathematics(all)
- Computational Mathematics
- Mathematics(all)
- Applied Mathematics
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In: Journal of Computational and Applied Mathematics, Vol. 187, No. 1, 01.03.2006, p. 96-122.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - ECT-B-splines defined by generalized divided differences
AU - Mühlbach, G.
PY - 2006/3/1
Y1 - 2006/3/1
N2 - ECT-spline curves are 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 ECT-splines consisting of functions having minimal compact supports, normalized either to form a nonnegative partition of unity or to have integral one. In this paper such ECT-B-splines are defined by generalized divided differences. This definition reduces to the classical one in case of a Schoenberg space. Under suitable assumptions it leads to a recursive method for computing the ECT-B-splines that reduces to the de Boor-Mansion-Cox recursion in case of ordinary polynomial splines and to Lyche's recursion in case of Tchebycheff splines [Mühlbach and Tang, Calculation of ECT-B-splines and of ECT-spline curves recursively, in preparation]. There is an ECT-spline space naturally adjoint to every ECT-spline space. We also construct B-splines via generalized divided differences for this space and study relations between the two adjoint spaces.
AB - ECT-spline curves are 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 ECT-splines consisting of functions having minimal compact supports, normalized either to form a nonnegative partition of unity or to have integral one. In this paper such ECT-B-splines are defined by generalized divided differences. This definition reduces to the classical one in case of a Schoenberg space. Under suitable assumptions it leads to a recursive method for computing the ECT-B-splines that reduces to the de Boor-Mansion-Cox recursion in case of ordinary polynomial splines and to Lyche's recursion in case of Tchebycheff splines [Mühlbach and Tang, Calculation of ECT-B-splines and of ECT-spline curves recursively, in preparation]. There is an ECT-spline space naturally adjoint to every ECT-spline space. We also construct B-splines via generalized divided differences for this space and study relations between the two adjoint spaces.
KW - ECT-B-splines
KW - ECT-systems
KW - Generalized divided differences
UR - http://www.scopus.com/inward/record.url?scp=27344445167&partnerID=8YFLogxK
U2 - 10.1016/j.cam.2005.03.040
DO - 10.1016/j.cam.2005.03.040
M3 - Article
AN - SCOPUS:27344445167
VL - 187
SP - 96
EP - 122
JO - Journal of Computational and Applied Mathematics
JF - Journal of Computational and Applied Mathematics
SN - 0377-0427
IS - 1
ER -