Curves from variational principles

Ch. A. Micchelli

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1992)

  • Volume: 26, Issue: 1, page 77-93
  • ISSN: 0764-583X

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Micchelli, Ch. A.. "Curves from variational principles." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 26.1 (1992): 77-93. <http://eudml.org/doc/193661>.

@article{Micchelli1992,
author = {Micchelli, Ch. A.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {curve modelling; curve design; variational principle; variational curve problems; convex duality theory; optimal curve; numerical examples; quadratic minimization problem},
language = {eng},
number = {1},
pages = {77-93},
publisher = {Dunod},
title = {Curves from variational principles},
url = {http://eudml.org/doc/193661},
volume = {26},
year = {1992},
}

TY - JOUR
AU - Micchelli, Ch. A.
TI - Curves from variational principles
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1992
PB - Dunod
VL - 26
IS - 1
SP - 77
EP - 93
LA - eng
KW - curve modelling; curve design; variational principle; variational curve problems; convex duality theory; optimal curve; numerical examples; quadratic minimization problem
UR - http://eudml.org/doc/193661
ER -

References

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  2. [2] G. FARIN, Curves and Surfaces for Computer Aided Geometric Design, A Practical Guide, Academic Press, 1988. Zbl0694.68004MR974109
  3. [3] T. A. FOLEY, Interpolation with Internal and Point Tension Controls Using Cubic Weighted v-splines, ACM Trans. Math. Software 13 (1987), pp. 68-96. Zbl0626.65008MR896535
  4. [4] T. A. FOLEY and G. M. NIELSON, Knot Selection for Parametric Spline Interpolation, in Mathematical Methods in Computer Aided Geometric Design, eds., T. Lyche and L. L. Schumaker, Academic Press, 1989, pp. 261-271. Zbl0677.41013MR1022713
  5. [5] R. FRANKE, Recent Advances in the Approximation of Surfaces from Scattered Data, in Topics in Multivanate Approximation, eds., C. K. Chui, L. L. Schumaker, and F. I. Utreras, Academic Press, Boston, 1987. Zbl0629.41021MR924824
  6. [6] J. W. JEROME, and S. D. FISHER, Minimum Norm Extremals in Function Spaces with Applications to Classical and Modern Analysis, Lecture Notes in Math. 479, Springer-Verlag, Berlin, 1975. Zbl0307.41027MR442780
  7. [7] S. KARLIN, Total Positivity, Vol. 1, Stanford University Press, Stanford, 1968. Zbl0219.47030MR230102
  8. [8] S. KARLIN, Interpolation Properties of Generalized Perfect Splines and the Solutions of Certain Extremal Problems I, Trans. Amer. Math. Soc., 206 (1975), pp. 25-66. Zbl0303.41011MR367512
  9. [9] L. D. LANDAU, and E. M. LIFSHITZ, Theory of Elasticity, Pergamon Press, New York, 1959. MR106584
  10. [10] E. H. LEE, and G. E. FORSYTHE, Variational Study of Nonlinear Spline Curves, SIAM Rev. 15 (1973), pp. 120-133. MR331716
  11. [11] S. MARIN, An Approach to Data Parametrization in Parametric Cubic Spline Interpolation Problems, J. Approx. Theory 41 (1984), pp. 64-86. Zbl0558.41006MR742237
  12. [12] C. A. MICCHELLI and F. I. UTRERAS, Smoothing and Interpolation in a Convex Set of Hilbert Space, SIAM. J. Sci. Stat. Comp. 9 (1988), pp. 728-746. Zbl0651.65046MR945935
  13. [13] G. M. NIELSON, Some Piecewise Polynomial Alternatives to Spline Under Tension, in Computer Aided Geometric Design, eds., R. E. Barnhill, and R. F. Riesenfeld, Academic Press (1974), pp. 209-235. MR371012
  14. [14] K. SCHERER, Best Interpolation with Free Nodes by Closed Curves, in Mathematical Methods in Computer Aided Geometric Design, eds., T. Lyche, and L. L. Schumaker, Academic Press, 1989, pp. 549-559. Zbl0675.41008MR1022734
  15. [15] G. S. SIDHU, and H. L. WEINERT, Vector-valued Lg-splines, J. Math. Anal., Appl. 70 (1979), pp. 505-529. Zbl0435.65007MR543591

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