Nested sequences of Chebyshev spaces and shape parameters
Marie-Laurence Mazure; Pierre-Jean Laurent
- Volume: 32, Issue: 6, page 773-788
- ISSN: 0764-583X
Access Full Article
topHow to cite
topMazure, Marie-Laurence, and Laurent, Pierre-Jean. "Nested sequences of Chebyshev spaces and shape parameters." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 32.6 (1998): 773-788. <http://eudml.org/doc/193898>.
@article{Mazure1998,
author = {Mazure, Marie-Laurence, Laurent, Pierre-Jean},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {Bézier points; blossoming; shape parameters; Chebyshev spaces},
language = {eng},
number = {6},
pages = {773-788},
publisher = {Dunod},
title = {Nested sequences of Chebyshev spaces and shape parameters},
url = {http://eudml.org/doc/193898},
volume = {32},
year = {1998},
}
TY - JOUR
AU - Mazure, Marie-Laurence
AU - Laurent, Pierre-Jean
TI - Nested sequences of Chebyshev spaces and shape parameters
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1998
PB - Dunod
VL - 32
IS - 6
SP - 773
EP - 788
LA - eng
KW - Bézier points; blossoming; shape parameters; Chebyshev spaces
UR - http://eudml.org/doc/193898
ER -
References
top- [1] P. J. BARRY, de Boor-Fix dual functionals and algorithms for Tchebycheffian B-spline curves, Constructive Approximation 12 (1996), 385-408. Zbl0854.41010MR1405005
- [2] P. J. BARRY, N. DYN, R. N. GOLDMAN and C. A. MICCHELLI, Identities for piecewise polynomial spaces determined by connection matrices, Aequationes Mathematicae 42 (1991), 123-136. Zbl0769.41007MR1125625
- [3] D. BISTER and H. PRAUTZSCH, A new approach to Tchebycheffian B-splines, in Curves and Surfaces with Applications to CAGD, Vanderbilt University Press (1997), 35-42. Zbl0938.65020MR1659765
- [4] N. DYN, A. EDELMAN and C. A. MICHELLI, On locally supported basis functions for the representation of geometrically continuous curves, Analysis 7 (1987), 313-341. Zbl0633.41005MR928645
- [5] N. DYN and A. RON, Recurrence relations for Tchebycheffian B-splines, Journal d'Analyse Mathématique 51 (1988), 118-138. Zbl0675.41021MR963152
- [6] S. KARLIN, Total Positivity, Stanford University Press, Stanford, 1968. Zbl0219.47030MR230102
- [7] S. KARLIN and W. J. STUDDEN, Tchebycheff Systems, Wiley Interscience, New York, 1966. Zbl0153.38902MR204922
- [8] S. KARLIN and Z. ZIEGLER, Chebyshevian spline functions, SIAM Journal Numerical Analysis 3 (1966), 514-543. Zbl0171.31002MR216206
- [9] R. KULKARNI and P.-J. LAURENT, Q-splines, Numerical Algorithms 1 (1991), 45-74. Zbl0797.65003MR1135287
- [10] R. KULKARNI, P.-J. LAURENT and M.-L. MAZURE, Non affine blossoms and subdivision for Q-splines, in Math. Methods in Computer Aided Geometric Design II, Academic Press, New York, 1992, 367-380. MR1172817
- [11] P.-J. LAURENT, M.-L. MAZURE and V. T. MAXIM, Chebyshev splines and shape parameters, RR 980M IMAG, Université Joseph Fourier, Grenoble, September 1997, Numerical Algorithms 15 (1997), 373-383. Zbl0891.65013MR1605676
- [12] P.-J. LAURENT, M.-L. MAZURE and G. MORIN, Shape effects with polynomial Chebyshev splines, in Curves and Surfaces with Applications in CAGD, Vanderbilt University Press, 1997, 255-262. Zbl0938.65019MR1659752
- [13] T. LYCHE, A recurrence relation for Chebyshevian B-splines, Constructive Approximation 1 (1985), 155-173. Zbl0583.41011MR891537
- [14] M.-L. MAZURE, Blossoming of Chebyshev splines, In Mathematical Methods for Curves and Surfaces, Vanderbilt University Press, 1995, 355-364. Zbl0835.65033MR1356981
- [15] M.-L. MAZURE, Chebyshev spaces, RR 952M IMAG, Université Joseph Fourier, Grenoble, January 1996.
- [16] M.-L. MAZURE, Chebyshev blossoming, RR 953M IMAG, Université Joseph Fourier, Grenoble, January 1996.
- [17] M.-L. MAZURE, Blossoming: a geometric approach, RR 968M IMAG, Université Joseph Fourier, Grenoble, January 1997, to appear in Constructive Approximation. Zbl0924.65010MR1660085
- [18] M.-L. MAZURE, Vandermonde type determinants and blossoming, The Fourth International Conference on Mathematical Methods for Curves and Surfaces, Lillehammer, Norway, July 3-8, 1997, RR 979M IMAG, Université Joseph Fourier, Grenoble, September 1997, Advances in Computational Math. 8 (1998), 291-315. Zbl0906.65014MR1637609
- [19] M.-L. MAZURE and P.-J. LAURENT, Affine and non affine blossoms, in Computational Geometry, World Scientific, 1993, 201-230. MR1339313
- [20] M.-L. MAZURE and P.-J. LAURENT, Marsden identities, blossoming and de Boor-Fix formula, in Advanced Topics in Multivariate Approximation, World Scientific Pub., 1996, 227-242. Zbl1273.41029MR1661413
- [21] M.-L. MAZURE and P.-J. LAURENT, Piecewise smooth spaces in duality: application to blossoming, RR696-M, IMAG, Université Joseph Fourier, Grenoble, January 1997, to appear in Journal of Approximation Theory. Zbl0952.41010MR1692244
- [22] M.-L. MAZURE and P.-J. LAURENT, Polynomial Chebyshev Splines, to appear. Zbl0916.68152MR1688408
- [23] M.-L. MAZURE and H. POTTMANN, Tchebycheff curves, in Total Positivity and its Applications, Kluwer Academic Pub. (1996), 187-218. Zbl0902.41018MR1421603
- [24] C. A. MICCHELLI, Mathematical Aspects of Geometric Modeling, CBMS-NSF Regional Conference Series in Applied Math. 65, SIAM, Philadelphie, 1995. Zbl0864.65008MR1308048
- [25] H. POTTMANN, The geometry of Tchebycheffian splines, Computer Aided Geometric Design 10 (1993), 181-210. Zbl0777.41016MR1235152
- [26] H. POTTMANN and M. G. WAGNER, Helix splines as an example of affine Tchebycheffian splines, Advances in Computational Math. 2 (1994), 123-142. Zbl0832.65008MR1266027
- [27] L. RAMSHAW, Blossoms are polar forms, Computer Aided Geometric Design 6 (1989), 323-358. Zbl0705.65008MR1030618
- [28] L. L. SCHUMAKER, Spline Functions: Basic Theory, Wiley Interscience, New York, 1981. Zbl0449.41004MR606200
- [29] H.-P. SEIDEL, New algorithms and techniques for Computing with geometrically continuous spline curves of arbitrary degree, Math. Modelling and Numerical Analysis 26 (1992), 149-176. Zbl0752.65008MR1155005
- [30] M. G. WAGNER and H. POTTMANN, Symmetric Tchebycheffian B-splines schemes, in Curves and Surfaces in Geometric Design, A. K. Peters, Wellesley, MA, 1994, 483-490. Zbl0814.65008MR1302230
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.