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B-splines and optimal stability

Author: J. M. Peña
Journal: Math. Comp. 66 (1997), 1555-1560
MSC (1991): Primary 65D07, 41A15
MathSciNet review: 1433268
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Abstract: It is proved that, among all nonnegative bases of its space, the B-spline basis is optimally stable for evaluating spline functions.

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  • [1] C. de Boor, The exact condition of the B-spline basis may be hard to determine, J. Approx. Theory 60 (1990), 334-359. MR 91h:65023
  • [2] J. M. Carnicer and J. M. Peña, Shape preserving representations and optimality of the Bernstein basis, Adv. Comput. Math. 1 (1993), 173-196.MR 94i:65138
  • [3] J. M. Carnicer and J. M. Peña, Least supported bases and local linear independence, Numer. Math. 67 (1994), 289-301. MR 95d:65012
  • [4] J. M. Carnicer and J. M. Peña, Totally positive bases for shape preserving curve design and optimality of B-splines, Comput. Aided Geom. Design 11 (1994), 633-654. MR 95i:65033
  • [5] J. M. Carnicer and J. M. Peña, Total positivity and optimal bases, Total positivity and its applications (M. Gasca, C.A. Micchelli, eds.), Kluwer Academic Press, Dordrecht, 1996, pp. 133-155. CMP 97:04
  • [6] R. T. Farouki and T. N. T. Goodman, On the optimal stability of the Bernstein basis, Math. Comp. 65 (1996), 1553-1566. MR 97a:65021
  • [7] R. T. Farouki and V. T. Rajan, On the numerical condition of polynomials in Bernstein form, Comput. Aided Geom. Design 4 (1987), 191-216. MR 89a:65028
  • [8] T. Lyche, Condition Numbers for B-splines, Numerical Analysis 1989 (D. F. Griffiths and
    G. A. Watson, eds.), Longman Scientific and Technical, Essex, 1990, pp. 182-192. CMP 91:17
  • [9] L. L. Schumaker, Spline Functions: Basic Theory, John Wiley and Sons, New York, 1981.MR 82j:41001

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Additional Information

J. M. Peña
Affiliation: Departamento de Matemática Aplicada, Universidad de Zaragoza, 50009 Zaragoza, Spain

Keywords: B-splines; optimal stability, condition number, nonnegative matrices, partial ordering
Received by editor(s): May 10, 1995
Received by editor(s) in revised form: July 29, 1996
Additional Notes: This work was partially supported by the Spanish Research Grant DGICYT PB93-0310 and by the EU project CHRX-CT94-0522.
Article copyright: © Copyright 1997 American Mathematical Society

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