Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2018, Volume 155, Pages 3–19 (Mi into387)  
This article is cited in 2 scientific papers (total in 2 papers)

Classification and applications of randomized functional numerical algorithms for the solution of second-kind Fredholm integral equations

A. V. Voitishekab

a Institute of Computational Mathematics and Mathematical Geophysics of Siberian Branch of Russian Academy of Sciences, Novosibirsk
b Novosibirsk State University
Full-text PDF (274 kB) Citations (2) English version article
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Abstract: Systematization of numerical randomized functional algorithms for approximation of solutions to second-kind Fredholm integral equation is performed in this paper. Three types of algorithms are emphasized: projection algorithms, grid algorithms, and projection-grid algorithms. Disadvantages of grid algorithms that require calculation of values of the kernel of integral equations at fixed points are revealed (practically, the kernels of equation have integrable singularities and this calculation is impossible). Thus, for applied problems related to the solution of second-kind Fredholm integral equations, projection or projection-grid randomized algorithms are more convenient.
Keywords: second-kind Fredholm integral equation, numerical solution, randomized algorithm, projection algorithm, grid algorithm, computational kernel.
English version:
Journal of Mathematical Sciences (New York), 2021, Volume 254, Issue 5, Pages 589–605
DOI: https://doi.org/10.1007/s10958-021-05328-z
Bibliographic databases:
Document Type: Article
UDC: 519.676
MSC: 65C40, 45B05, 65C05
Language: Russian
Citation: A. V. Voitishek, “Classification and applications of randomized functional numerical algorithms for the solution of second-kind Fredholm integral equations”, Mathematical Analysis, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 155, VINITI, Moscow, 2018, 3–19; J. Math. Sci. (N. Y.), 254:5 (2021), 589–605
Citation in format AMSBIB
\Bibitem{Voi18}
\by A.~V.~Voitishek
\paper Classification and applications of randomized functional numerical algorithms for the solution of second-kind Fredholm integral equations
\inbook Mathematical Analysis
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2018
\vol 155
\pages 3--19
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into387}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=3904902}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2021
\vol 254
\issue 5
\pages 589--605
\crossref{https://doi.org/10.1007/s10958-021-05328-z}
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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