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

How to cite

top

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

top
  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. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.