Elementary spline functions

Authors

  • Gheorghe Coman Babeş-Bolyai University, Cluj-Napoca, Romania
  • Teodora Cătinaş Babeş-Bolyai University, Cluj-Napoca, Romania

DOI:

https://doi.org/10.33993/jnaat372-886

Keywords:

elementary spline function, Cauchy problem, error estimation
Abstract views: 185

Abstract

The aim of this paper is to define the elementary spline functions in analogy with the definition of the polynomial spline functions, given by I. J.Schonberg. Also, it is described a method for constructing the elementary spline functions. Finally, some examples are given.

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References

Coman, Gh., Numerical Analysis, Ed. Libris, Cluj-Napoca, 1995 (in Romanian).

Ionescu, D. V., Applications of the succesive approximation method to the numerical integration of differential equations, Studii şi cercetări matematice, Cluj-Napoca, 11, pp. 273-286, 1960 (in Romanian).

Pavel, G., The approximative solution of the Cauchy problem for a linear differential equation of order n, Studia Universitatis Babeş-Bolyai, Mathematica, no. 2, pp. 49-53, 1978 (in Romanian).

Popoviciu, T., Notes sur les fonctions convexes d'ordre superieur, Bull. Math. de la Societe Roumaine des Science, 43, pp. 95-141, 1941.

Rus, I. A., Differential equations, integral equations and dynamical systems, Ed. House Transilvania Press, Cluj-Napoca, 1996.

Schonberg, I. J., Contributions to the problem of approximations of equidistant data by analytic functions, Quart. Appl. Math., 4, no. 1, pp. 45-99, 1946, https://doi.org/10.1090/qam/15914 DOI: https://doi.org/10.1090/qam/15914

Schonberg, I. J., Spline functions, convex curves and mechanical quadrature, Bull. Amer. Math. Soc., 64, no. 1, pp. 352-357, 1958, https://doi.org/10.1090/s0002-9904-1958-10227-x DOI: https://doi.org/10.1090/S0002-9904-1958-10227-X

Schonberg, I. J., On trigonometric spline interpolation, J. Mathematics and Mechanics, 13, no. 5, pp. 795-825, 1964, https://www.jstor.org/stable/24901234

Schonberg, I. J., On spline interpolation at all integer points of the real axis, Mathematica, 10 (33), no. 1, pp. 151-170, 1968,

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Published

2008-08-01

How to Cite

Coman, G., & Cătinaş, T. (2008). Elementary spline functions. Rev. Anal. Numér. Théor. Approx., 37(2), 143–149. https://doi.org/10.33993/jnaat372-886

Issue

Vol. 37 No. 2 (2008)

Section

Articles

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Copyright (c) 2015 Journal of Numerical Analysis and Approximation Theory

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