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

Jochen Schmidt

Banach Center Publications (1994)

  • Volume: 29, Issue: 1, page 35-44
  • ISSN: 0137-6934

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Schmidt, Jochen. "Dual algorithms for convex approximations of histograms using cubic C¹-splines." Banach Center Publications 29.1 (1994): 35-44. <http://eudml.org/doc/262596>.

@article{Schmidt1994,
author = {Schmidt, Jochen},
journal = {Banach Center Publications},
keywords = {dual algorithms; convex approximations; histograms; smoothing; interpolation; cubic splines; piecewise cubic polynomial function; Frenchel conjugates; constrained minimization},
language = {eng},
number = {1},
pages = {35-44},
title = {Dual algorithms for convex approximations of histograms using cubic C¹-splines},
url = {http://eudml.org/doc/262596},
volume = {29},
year = {1994},
}

TY - JOUR
AU - Schmidt, Jochen
TI - Dual algorithms for convex approximations of histograms using cubic C¹-splines
JO - Banach Center Publications
PY - 1994
VL - 29
IS - 1
SP - 35
EP - 44
LA - eng
KW - dual algorithms; convex approximations; histograms; smoothing; interpolation; cubic splines; piecewise cubic polynomial function; Frenchel conjugates; constrained minimization
UR - http://eudml.org/doc/262596
ER -

References

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  1. [CM84] P. Costantini and R. Morandi, Monotone and convex cubic spline interpolation, Calcolo 21 (1984), 281-294. Zbl0565.41006
  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. Zbl0662.41008
  3. [FC80] F. N. Fritsch and R. E. Carlson, Monotone piecewise cubic interpolation, SIAM J. Numer. Anal. 17 (1980), 238-246. Zbl0423.65011
  4. [MC89] R. Morandi and P. Costantini, Piecewise monotone quadratic histosplines, SIAM J. Sci. Statist. Comput. 10 (1989), 397-406. Zbl0671.65008
  5. [N78] E. Neuman, Uniform approximation by some Hermite interpolating splines, J. Comput. Appl. Math. 4 (1978), 7-9. Zbl0388.41007
  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. Zbl0643.65005
  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. Zbl0757.65007
  10. [S92a] J. W. Schmidt, Dual algorithms for solving convex partially separable optimization problems, Jahresber. Deutsch. Math.-Verein. 94 (1992) 40-62. Zbl0751.90060
  11. [S93] J. W. Schmidt, Positive, monotone, and S-convex C¹-histopolation on rectangular grids, Computing 50 (1993), 19-30. Zbl0770.65003
  12. [SH84] J. W. Schmidt und W. Heß, Schwach verkoppelte Ungleichungssysteme und konvexe Spline-Interpolation, Elem. Math. 39 (1984), 85-95. Zbl0518.65040
  13. [SH88] J. W. Schmidt und W. Heß, Positivity of cubic polynomials on intervals and positive spline interpolation, BIT 28 (1988), 340-352. Zbl0642.41007
  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. Zbl0721.65002
  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. Zbl0147.32102
  18. [Sp90] H. Späth, Eindimensionale Spline-Interpolations-Algorithmen, R. Oldenbourg-Verlag, München-Wien 1990. 

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