Unified representations of nonlinear splines

Journal of Approximation Theory

Volumn 84, Issue 3, 1996, Pages 315-350

  Linnér, Anders ^a  

^a NORTHERN ILLINOIS UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030097916     PISSN: 00219045     EISSN: None     Source Type: Journal    
DOI: 10.1006/jath.1996.0022     Document Type: Article

References (16)

1. 1. G. BIRKHOFF AND C. DE BOOR, Piecewise polynomial interpolation and approximation, in "Approximation of Functions" (H. L. Garabedian, Ed.), pp. 164-190, Elsevier, New York/ Amsterdam, 1965.
2. 2. G. BRUNNETT, A new characterization of plane elastica, in "Mathematical Methods in Computer Aided Geometric Design II" (T. Lyche and L. Schumaker, Eds.), pp. 43-56, Academic Press, New York, 1992.
3. 3. G. BRUNNETT, "The Curvature of Plane Elastic Curves," Tech. Report NPS-MA-93-013, Naval Postgraduate School, 1993.
4. 4. G. BRUNNETT, Properties of minimal energy splines, in "Curve and Surve Design" (H. Hagen, Ed.), pp. 3-22, SIAM, Philadelphia, 1992.
5. 5. M. GOLOMB AND J. W. JEROME, Equilibria of the curvature functional and manifolds of nonlinear interpolating spline curves, SIAM J. Math. Anal. 13 (1982), 421-458.
6. 6. B. K. P. HORN, The curve of least energy, ACM Trans. Math. Software 9 (1983), 441-460.
7. 7. J. W. JEROME, Minimization problems and linear and nonlinear spline functions. I. Existence, SIAM J. Numer. Anal. 10 (1973), 808-819.
8. 8. J. W. JEROME, Smooth interpolating curves of prescribed length and minimum curvature, Proc. Amer. Math. Soc. 51 (1975), 62-66.
9. 9. E. D. JOU AND W. HAN, Minimal-energy splines. I. Plane curves with angle constraints, Math. Methods Appl. Sci. 13 (1990), 351-372.
10. 10. J. LANGER AND D. A. SINGER, Curve-straightening and a minimax argument for closed elastic curves, Topology 24 (1985), 75-88.
11. 11. E. H. LEE AND G. E. FORSYTHE, Variational study of nonlinear spline curves, SIAM Rev. 15 (1973), 120-133.
12. 12. A. LINNÉR, Some properties of the curve straightening flow in the plane, Trans. Amer. Math. Soc. 314, No. 2 (1989), 605-617.
13. 2 defined on curves in the plane with arbitrary types of boundary conditions, in "Geometric Analysis and Computer Graphics," MSRI Publ., Vol. 17, pp. 127-138, Springer-Verlag, New York/ Berlin, 1991.
14. 14. A. LINNÉR, Curve-straightening in closed Euclidean submanifolds, Commun. Math. Phys. 138 (1991), 33-49.
15. 15. A. LINNÉR, Curve-straightening, in "Proc. Symp. Pure Math.," Vol. 54, III, pp. 451-158, Amer. Math. Soc., Providence, RI, 1993.
16. 16. A. LINNÉR, Existence of free non-closed Euler-Bernoulli elastica, Nonlinear Anal. 21, No. 8 (1993), 575-593.