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Computational Mathematics and Mathematical Physics

, Volume 58, Issue 11, pp 1708–1715 | Cite as

On One Problem of Calculating a Two-Dimensional Convolution with an Exponential Kernel

  • A. A. Korotkin
  • A. A. Maksimov
  • N. A. Strelkov
Article
  • 10 Downloads

Abstract

The paper presents an algorithm for calculating a two-dimensional discrete convolution with an exponential kernel by solving a boundary value problem for an equation with a second-order finite-difference operator. To solve the boundary value problem, a one-step iterative process converging with a rate of a geometric progression is developed.

Keywords:

two-dimensional discrete convolution finite-difference operator boundary value problem 

Notes

REFERENCES

  1. 1.
    D. E. Dudgeon and R. M. Mersereau, Multidimensional Digital Signal Processing (Prentice-Hall Signal, Englewood Cliffs, N.J., 1983).zbMATHGoogle Scholar
  2. 2.
    Methods for Digital Image Processing, Ed. by V. A. Soifer (Fizmatlit, Moscow, 2003) [in Russian].Google Scholar
  3. 3.
    H. J. Nussbaumer, Fast Fourier Transform and Convolution Algorithms (Springer-Verlag, Heidelberg, 1990).zbMATHGoogle Scholar
  4. 4.
    D. H. Eberly, GPGPU Programming for Games and Science (CRC, Boca Raton, 2014).CrossRefGoogle Scholar
  5. 5.
    A. K. Karlin, A. A. Korotkin, and N. A. Strelkov, Cellular neural network in the problem of filtering a two-dimensional signal," Model. Anal. Inf. Sist. 7 (2), 38–43 (2000).Google Scholar
  6. 6.
    A. A. Samarskii, The Theory of Difference Schemes (Nauka, Moscow, 1977; Marcel Dekker, New York, 2001).Google Scholar
  7. 7.
    A. A. Samarskii and E. S. Nikolaev, Numerical Methods for Grid Equations (Nauka, Moscow, 1978; Birkhäuser, Basel, 1989).Google Scholar
  8. 8.
    E. F. Beckenbach and R. Bellman, Inequalities (Springer-Verlag, Berlin, 1961).CrossRefzbMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Yaroslavl State UniversityYaroslavlRussia

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