Abstract
This paper deals with cases when the values of derivatives of a function are given at grid nodes or the values of integrals of a function over grid intervals are known. Polynomial and trigonometric integrodifferential splines for computing the value of a function from given values of its nodal derivatives and/or from its integrals over grid intervals are constructed. Error estimates are obtained, and numerical results are presented.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
V. I. Kireev and T. K. Biryukova, “Polynomial integrodifferential one- and two-dimensional splines,” Vychisl. Tekhnol. 3(3), 19–34 (1998).
V. I. Kireev and A. V. Panteleev, Numerical Methods in Examples and Problems (Vysshaya Shkola, Moscow, 2008) [in Russian].
I. G. Burova, Approximations by Real and Complex Minimal Splines (Sankt-Peterburg. Gos. Univ., St. Petersburg, 2013) [in Russian].
S. G. Mikhlin, “Variational-difference approximation,” Zap. Nauchn. Semin. LOMI 48, 32–188 (1974).
Yu. S. Zav’yalov, B. I. Kvasov, and V. L. Miroshnichenko, Spline Function Methods (Fizmatlit, Moscow, 1980) [in Russian].
D. K. Faddeev and I. S. Sominskii, Problem Book in Higher Algebra (Nauka, Moscow, 1972) [in Russian].
G. E. Forsythe, M. A. Malcolm, and C. B. Moler, Computer Methods for Mathematical Computations (Prentice Hall, Englewood Cliffs, N.J., 1977; Mir, Moscow, 1980).
V. S. Ryaben’kii, An Introduction to Computational Mathematics (Fizmatlit, Moscow, 1994) [in Russian].
A. V. Dimaki and A. A. Svetlakov, “Approximation of probability densities of random variables with the use of orthogonal Chebyshev-Hermite polynomials,” Izv. Tomsk. Politekh. Univ. 309(8), 6–11 (2006).
I. S. Berezin and N. P. Zhidkov, Computing Methods (Fizmatgiz, Moscow, 1962; Pergamon, Oxford, 1965), Vol. 1.
A. G. Sergeev and V. V. Krokhin, Metrology (Logos, Moscow, 2001) [in Russian].
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © I.G. Burova, O.V. Rodnikova, 2014, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2014, Vol. 54, No. 12, pp. 1966–1978.
Rights and permissions
About this article
Cite this article
Burova, I.G., Rodnikova, O.V. Application of integrodifferential splines to solving an interpolation problem. Comput. Math. and Math. Phys. 54, 1903–1914 (2014). https://doi.org/10.1134/S0965542514120094
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0965542514120094