Details
| Original language | English |
|---|---|
| Pages (from-to) | 259-283 |
| Number of pages | 25 |
| Journal | Numerical algorithms |
| Volume | 38 |
| Issue number | 4 |
| Publication status | Published - 2005 |
Abstract
Cardinal ECT-spline curves are generated from one ECT-system of order n which is shifted by integer translations via one connection matrix. If this matrix is nonsingular, lower triangular and totally positive, there exists an ECT-B-spline function N 0 n (x) having minimal compact support [0,n] whose integer translates span the cardinal ECT-spline space. This B-spline is computed explicitly piece by piece. Involved is the characteristic polynomial of a certain matrix which is the product of a matrix related to the connection matrix and of the generalized Taylor matrix of the basic ECT-system. This approach extends results for polynomial cardinal splines via connection matrices [6] to the more general setting of cardinal ECT-splines. The method is illustrated by two examples based on ECT-systems of rational functions with prescribed poles. Also, a Green's function involved is expressed explicitly as an ECT-B-splines series.
Keywords
- Cardinal ECT-B-splines, Cardinal ECT-spline curves, ECT-B-splines, ECT-systems
ASJC Scopus subject areas
- Mathematics(all)
- Applied Mathematics
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In: Numerical algorithms, Vol. 38, No. 4, 2005, p. 259-283.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Cardinal ECT-splines
AU - Tang, Yuehong
AU - Mühlbach, Günter W.
PY - 2005
Y1 - 2005
N2 - Cardinal ECT-spline curves are generated from one ECT-system of order n which is shifted by integer translations via one connection matrix. If this matrix is nonsingular, lower triangular and totally positive, there exists an ECT-B-spline function N 0 n (x) having minimal compact support [0,n] whose integer translates span the cardinal ECT-spline space. This B-spline is computed explicitly piece by piece. Involved is the characteristic polynomial of a certain matrix which is the product of a matrix related to the connection matrix and of the generalized Taylor matrix of the basic ECT-system. This approach extends results for polynomial cardinal splines via connection matrices [6] to the more general setting of cardinal ECT-splines. The method is illustrated by two examples based on ECT-systems of rational functions with prescribed poles. Also, a Green's function involved is expressed explicitly as an ECT-B-splines series.
AB - Cardinal ECT-spline curves are generated from one ECT-system of order n which is shifted by integer translations via one connection matrix. If this matrix is nonsingular, lower triangular and totally positive, there exists an ECT-B-spline function N 0 n (x) having minimal compact support [0,n] whose integer translates span the cardinal ECT-spline space. This B-spline is computed explicitly piece by piece. Involved is the characteristic polynomial of a certain matrix which is the product of a matrix related to the connection matrix and of the generalized Taylor matrix of the basic ECT-system. This approach extends results for polynomial cardinal splines via connection matrices [6] to the more general setting of cardinal ECT-splines. The method is illustrated by two examples based on ECT-systems of rational functions with prescribed poles. Also, a Green's function involved is expressed explicitly as an ECT-B-splines series.
KW - Cardinal ECT-B-splines
KW - Cardinal ECT-spline curves
KW - ECT-B-splines
KW - ECT-systems
UR - http://www.scopus.com/inward/record.url?scp=24044440954&partnerID=8YFLogxK
U2 - 10.1007/s11075-004-5301-6
DO - 10.1007/s11075-004-5301-6
M3 - Article
AN - SCOPUS:24044440954
VL - 38
SP - 259
EP - 283
JO - Numerical algorithms
JF - Numerical algorithms
SN - 1017-1398
IS - 4
ER -