GB-splines of arbitrary order

Journal of Computational and Applied Mathematics

Volumn 104, Issue 1, 1999, Pages 63-88

  Ksasov, Boris I ^a   Sattayatham, Pairote ^b  

^a INSTITUTE OF COMPUTATIONAL TECHNOLOGIES   (Russian Federation)

^b SURANAREE UNIVERSITY OF TECHNOLOGY   (Thailand)

Author keywords

GB spline; Shape preserving approximation; Spline; Variation diminishing; Weak Chebyshevian system

Indexed keywords

CHEBYSHEV APPROXIMATION; CURVE FITTING; INTERPOLATION; MATHEMATICAL TRANSFORMATIONS;

CHEBYSHEVIAN SPLINES; SHAPE-PRESERVING APPROXIMATION; VARIATION DIMINISHING;

GRAPH THEORY;

EID: 0032676403     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0427(98)00265-9     Document Type: Article

References (15)

1. C. de Boor, A Practical Guide to Splines, Springer, New York, 1978.
2. C. de Boor, A. Pinkus, Backward error analysis for totally positive linear systems, Numer. Math. 27 (1977) 485-490.
3. N. Dyn, A. Ron, Recurrence relations for Tchebicheffian B-splines, J. Anal. Math. 51 (1988) 118-138.
4. F.R. Gantmacher, The Theory of Matrices, vol. 1, Chelsea Publishing Company, New York, 1960.
5. A. Gresbrand, A recurrence relation for rational B-splines with prescribed poles, preprint.
6. S. Karlin, Total Positivity, vol. 1, Stanford University Press, Stanford, CA, 1968.
7. P.E. Koch, T. Lyche, Exponential B-splines in tension, in: C.K. Chui, L.L. Schumaker, J.D. Ward (Eds.), Approximation Theory VI, vol. II, Academic Press, Boston, 1989, pp. 361-364.
8. P.E. Koch, T. Lyche, Construction of exponential tension B-splines of arbitrary order, in: P.J. Laurent, A. Le Méhaute, L.L. Schumaker (Eds.), Curves and Surfaces, Academic Press, New York, 1991, pp. 255-258.
9. P.E. Koch, T. Lyche, Interpolation with exponential B-splines in tension, in: G. Farin et al. (Eds.), Geometric Modelling, Computing/Supplementum, vol. 8, Springer, Wien, 1993 pp. 173-190.
10. B.I. Ksasov, Local bases for generalized cubic splines, Russian J. Numer. Anal. Math. Modelling 10 (1995) 49-80.
11. B.I. Ksasov, Shape preserving spline approximation via local algorithms, in: F. Fontanella, K. Jetter, P.J. Laurent (Eds.), Advanced Topics in Multivariate Approximation, World Scientific, Singapore, 1996, pp. 181-196,
12. B.I. Kvasov, GB-splines and their properties, Ann. Numer. Math. 3 (1996) 139-149.
13. T. Lyche, A recurrence relation for Chebyshevian B-splines, Constr. Approx. 1 (1985) 155-173.
14. L.L. Schumaker, Spline Functions: Basic Theory, Wiley, New York, 1981.
15. L.L. Schumaker, On recurrences for generalized B-splines, J. Approx. Theory 36 (1982) 16-31.