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Title

Dual algorithms for convex approximations of histograms using cubic C¹-splines

Authors 1

Affiliations

  1. Institute of Numerical Analysis, Technical University of Dresden, Mommsenstr. 13, D-01062 Dresden, Germany

Bibliography

  1. [CM84] P. Costantini and R. Morandi, Monotone and convex cubic spline interpolation, Calcolo 21 (1984), 281-294.
  2. [DS85] S. Dietze and J. W. Schmidt, Determination of shape preserving spline interpolants with minimal curvature via dual programs, J. Approx. Theory 52 (1988), 43-57.
  3. [FC80] F. N. Fritsch and R. E. Carlson, Monotone piecewise cubic interpolation, SIAM J. Numer. Anal. 17 (1980), 238-246.
  4. [MC89] R. Morandi and P. Costantini, Piecewise monotone quadratic histosplines, SIAM J. Sci. Statist. Comput. 10 (1989), 397-406.
  5. [N78] E. Neuman, Uniform approximation by some Hermite interpolating splines, J. Comput. Appl. Math. 4 (1978), 7-9.
  6. [N82] E. Neuman, Shape preserving interpolation by polynomial splines, Wrocław Univ., Inst. of Comput. Sci. Report No. 122 (1982).
  7. [SU88] M. Sakai and R. A. Usmani, A shape preserving area true approximation of histograms by rational splines, BIT 28 (1988), 329-339.
  8. [S91] J. W. Schmidt, Beiträge zur konvexen Interpolation, Histopolation und Approximation durch Spline-Funktionen, Mitt. Math. Gesellsch. Hamburg 12 (1991), 603-628.
  9. [S92] J. W. Schmidt, Constrained smoothing of histograms by quadratic splines, Computing 48 (1992), 97-107.
  10. [S92a] J. W. Schmidt, Dual algorithms for solving convex partially separable optimization problems, Jahresber. Deutsch. Math.-Verein. 94 (1992) 40-62.
  11. [S93] J. W. Schmidt, Positive, monotone, and S-convex C¹-histopolation on rectangular grids, Computing 50 (1993), 19-30.
  12. [SH84] J. W. Schmidt und W. Heß, Schwach verkoppelte Ungleichungssysteme und konvexe Spline-Interpolation, Elem. Math. 39 (1984), 85-95.
  13. [SH88] J. W. Schmidt und W. Heß, Positivity of cubic polynomials on intervals and positive spline interpolation, BIT 28 (1988), 340-352.
  14. [SH91] J. W. Schmidt und W. Heß, Shape preserving C²-spline histopolation, Hamburger Beitr. Angew. Math., preprint A 41 (1991), and J. Approx. Theory, to appear.
  15. [SHN90] J. W. Schmidt, W. Heß and T. Nordheim, Shape preserving histopolation using rational quadratic splines, Computing 44 (1990), 245-258.
  16. [SS90] J. W. Schmidt and I. Scholz, A dual algorithm for convex-concave data smoothing with cubic C²-splines, Numer. Math. 57 (1990), 330-350.
  17. [Sh64] I. J. Schoenberg, Spline functions and the problem of graduation, Proc. Nat. Acad. Sci. U.S.A. 52 (1964), 947-950.
  18. [Sp90] H. Späth, Eindimensionale Spline-Interpolations-Algorithmen, R. Oldenbourg-Verlag, München-Wien 1990.
Banach Center Publications
1994/29/1
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Pages:
35-44
Main language of publication
English
Published
1994
Exact and natural sciences