60
Views
1
CrossRef citations to date
0
Altmetric
Original Articles

A generalization of the Remez algorithm to a class of linear spline approximation problems with constraints on spline parameters

Pages 793-810 | Received 26 Sep 2007, Published online: 17 Sep 2008

References

  • De Boor , C. 1978 . A Practical Guide to Splines , New-York, Heidelberg : Springer .
  • Chebyshev , P. L. 1955 . The Theory of Mechanisms Known as Parallelograms , 611 – 648 . Moscow : Publishing House of the USSR Academy of Sciences . (in Russian)
  • Ishkhanova , M. V. and Chistyakov , S. V. 1998 . Mathematical Modelling of Taxation Tables , St-Petersburg : State University Press .
  • Meinardus , G. , Nürnberger , G. , Sommer , M. and Strauss , H. 1989 . Algorithms for piecewise polynomials and splines with free knots . Math. Comput. , 53 ( 187 ) : 235 – 247 .
  • Nürnberger , G. and Sommer , M. 1983 . A Remez type algorithms for spline functions . Numer. Math. , 41 : 117 – 146 .
  • Nürnberger , G. 1989 . Approximation by Spline Functions , Berlin : Springer .
  • Nürnberger , G. , Sommer , M. Schumaker and Strauss , H. 1985 . Approximation by generalized splines . J. Math. Anal. Appl. , 108 : 466 – 494 .
  • Remez , E. Ya. 1962 . “ General computational methods of Chebyshev approximation. Problems with linear real parameters ” . Washington, DC : Translation available from the US Atomic Commission . Izv. Akad. Nauk Ukrain. SSR, Kiev, 1957
  • Soukhoroukova , N. V. 2001 . Necessary and sufficient optimality conditions for approximation continuous functions by functions from a special class on an interval . Vestnik St-Petersburg State Univ. , 1 ( 2 ) : 66 – 72 .
  • Soukhoroukova , N. V. 2003 . The problem of constructing a polynomial spline satisfying Chebyshev approximation conditions . Appl. Math. Mech. , 1 : 42 – 46 . (Joung Young Scientists)
  • Soukhoroukova , N. V. A generalisation of Vall’ee-Poussin theorem and exchange basis rules to the case of polynomia l splines . Proceedings of Stability and Control Processes SCP2005, Dedicated to the 75 years Anniversary of V.I. Zubov . Vol. 2 , pp. 948 – 958 .
  • Soukhoroukova , N. V. “ Uniform approximation by polynomial splines of the highest defect: necessary and sufficient optimality conditions and their generalisations ” . Research Rep., University of Ballarat, ITMS . available at http://www.ballarat.edu.au/ard/itms/publications/researchPapers/Papers2007/07-01.pdf
  • Tarashnin , M. G. 1996 . “ Application of the theory of quasidifferentials to solving approximation problems ” . St-Petersburg State University . Ph.D. diss

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.