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Numerical differentiation using spline functions

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An Erratum to this article was published on 30 January 2013

We consider the application of splines with minimum-norm derivative in numerical differentiation. Tabular functions are approximated by a cubic spline with a piecewise-continuous second derivative, which ensures high-accuracy evaluation of the derivative.

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References

  1. V. I. Dmitriev and Zh. G. Ingtem, “A two-dimensional minimum-derivative spline,” Computational Mathematics and Modeling, 21, No. 2, 206–211 (2010).

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  2. Zh. G. Ingtem, “Spline function with minimum-norm derivative in interpolation and approximation problems,” Vestnik MGU, Vychisl. Matem. Kibern., No. 4, 16–27 (2008).

  3. V. I. Dmitriev and Zh. Ingtem, “Solving an integral equation of the first kind by spline approximation,” Computational Mathematics and Modeling, 15, No. 2 (April–June 2004).

  4. A. N. Tikhonov, “Ill-posed problems and their solution,” in: Solution Methods of Ill-Posed Problems and Their Applications [in Russian], Proc. All-Union School of Young Scientists, MGU, Moscow (1974), pp. 6–11.

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Authors and Affiliations

  1. Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, Russia

    V. I. Dmitriev & Zh. G. Ingtem

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  1. V. I. Dmitriev
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  2. Zh. G. Ingtem
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Correspondence to V. I. Dmitriev.

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Translated from Prikladnaya Matematika i Informatika, No. 38, pp. 58–65, 2011.

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Dmitriev, V.I., Ingtem, Z.G. Numerical differentiation using spline functions. Comput Math Model 23, 312–318 (2012). https://doi.org/10.1007/s10598-012-9139-9

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  • DOI: https://doi.org/10.1007/s10598-012-9139-9

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