On the optimal stability of bases of univariate functions

Numerische Mathematik

Volumn 91, Issue 2, 2002, Pages 305-318

  Pena J M ^a  

^a UNIVERSITY OF ZARAGOZA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0036013091     PISSN: 0029599X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002110100327     Document Type: Article

References (18)

1. de Boor, C.: The exact condition of the B-spline basis may be hard to determine. J. Approx. Theory 60, 334-359 (1990)
2. Carnicer, J. M., Goodman, T. N. T. & Peña, J. M.: Support and foundation of bases. Ann. Numerical Math. 4, 161-180 (1997)
3. Carnicer J. M. & Peña, J. M.: Least supported bases and local linear independence. Numer. Math. 67, 289-301 (1994)
4. Carnicer J. M. & Peña, J. M: On transforming a Tchebycheff system into a strictly totally positive system. J. Approx. Theory 81, 274-295 (1995)
5. Carnicer J. M. & Peña, J. M.: Total positivity and optimal bases. Total positivity and its applications (M. Gasca, C.A. Micchelli, eds.). Dordrecht: Kluwer Academic Press, pp. 133-155 (1996)
6. Farouki, R. T. & Goodman, T. N. T.: On the optimal stability of Bernstein basis. Math. Comp. 65, 1553-1566 (1996)
7. Farouki, R. T. & Rajan, V. T.: On the numerical condition of polynomials in Bernstein form. Comput. Aided Geom. Design 4, 191-216 (1987)
8. Gonsor, D. & Neamtu, M.: Null spaces of differential operators, polar forms and splines. J. Approx. Theory 86, 81-107 (1996)
9. Karlin, S.: Total Positivity. Stanford: Stanford Univ. Press, 1968
10. Karlin, S. & Studden, W.: Tchebycheff Systems: With Applications in Analysis and Statistics. New York: Interscience, 1966
11. Lyche, T.: Condition Numbers for B-splines. Numerical Analysis 1989 (D. F. Griffiths and G. A. Watson, eds.). Essex: Pittman Research Notes in Mathematics Series 228, Longman Scientific and Technical, pp. 182-192 (1990)
12. Lyche, T. & Winther, R.: A stable recurrence relation for trigonometric B-splines. J. Approx. Theory 25, 266-279 (1979)
13. Mink, H.: Nonnegative matrices. New York: Wiley Interscience, 1988
14. Peña, J. M.: Shape preserving representations for trigonometric polynomial curves. Comput. Aided Geometric Des. 14, 5-11 (1997)
15. Peña, J. M.: B-splines and optimal stability. Math. Comp. 66, 1555-1560 (1997)
16. Schumaker, L. L.: Spline Functions: Basic Theory. New York: John Wiley and Sons, 1981
17. Walz, G.: Some identities for trigonometric B-splines with an application to curve design. BIT 37, 189-201 (1997)
18. Zielke, R.: Discontinuous Čebyšev systems. New York: Lecture Notes in Mathematics 707. Berlin Heidelberg New York: Springer, 1979