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On randomized algorithms for numerical solution of applied Fredholm integral equations of the second kind. / Voytishek, Anton V.; Shipilov, Nikolay M.

Proceedings of the 8th International Conference on Mathematical Modeling, ICMM 2017. ред. / IE Egorov; SV Popov; PN Vabishchevich; MY Antonov; NP Lazarev; MS Troeva; MS Troeva; AO Ivanova; YM Grigorev. Том 1907 American Institute of Physics Inc., 2017. 030015 (AIP Conference Proceedings; Том 1907).

Результаты исследований: Публикации в книгах, отчётах, сборниках, трудах конференцийстатья в сборнике материалов конференциинаучнаяРецензирование

Harvard

Voytishek, AV & Shipilov, NM 2017, On randomized algorithms for numerical solution of applied Fredholm integral equations of the second kind. в IE Egorov, SV Popov, PN Vabishchevich, MY Antonov, NP Lazarev, MS Troeva, MS Troeva, AO Ivanova & YM Grigorev (ред.), Proceedings of the 8th International Conference on Mathematical Modeling, ICMM 2017. Том. 1907, 030015, AIP Conference Proceedings, Том. 1907, American Institute of Physics Inc., 8th International Conference on Mathematical Modeling, ICMM 2017, Yakutsk, Российская Федерация, 04.07.2017. https://doi.org/10.1063/1.5012637

APA

Voytishek, A. V., & Shipilov, N. M. (2017). On randomized algorithms for numerical solution of applied Fredholm integral equations of the second kind. в IE. Egorov, SV. Popov, PN. Vabishchevich, MY. Antonov, NP. Lazarev, MS. Troeva, MS. Troeva, AO. Ivanova, & YM. Grigorev (Ред.), Proceedings of the 8th International Conference on Mathematical Modeling, ICMM 2017 (Том 1907). [030015] (AIP Conference Proceedings; Том 1907). American Institute of Physics Inc.. https://doi.org/10.1063/1.5012637

Vancouver

Voytishek AV, Shipilov NM. On randomized algorithms for numerical solution of applied Fredholm integral equations of the second kind. в Egorov IE, Popov SV, Vabishchevich PN, Antonov MY, Lazarev NP, Troeva MS, Troeva MS, Ivanova AO, Grigorev YM, Редакторы, Proceedings of the 8th International Conference on Mathematical Modeling, ICMM 2017. Том 1907. American Institute of Physics Inc. 2017. 030015. (AIP Conference Proceedings). doi: 10.1063/1.5012637

Author

Voytishek, Anton V. ; Shipilov, Nikolay M. / On randomized algorithms for numerical solution of applied Fredholm integral equations of the second kind. Proceedings of the 8th International Conference on Mathematical Modeling, ICMM 2017. Редактор / IE Egorov ; SV Popov ; PN Vabishchevich ; MY Antonov ; NP Lazarev ; MS Troeva ; MS Troeva ; AO Ivanova ; YM Grigorev. Том 1907 American Institute of Physics Inc., 2017. (AIP Conference Proceedings).

BibTeX

@inproceedings{905d7bf8ea1d41719c8c8afa62d9b4fd,
title = "On randomized algorithms for numerical solution of applied Fredholm integral equations of the second kind",
abstract = "In this paper, the systematization of numerical (implemented on a computer) randomized functional algorithms for approximation of a solution of Fredholm integral equation of the second kind is carried out. Wherein, three types of such algorithms are distinguished: the projection, the mesh and the projection-mesh methods. The possibilities for usage of these algorithms for solution of practically important problems is investigated in detail. The disadvantages of the mesh algorithms, related to the necessity of calculation values of the kernels of integral equations in fixed points, are identified. On practice, these kernels have integrated singularities, and calculation of their values is impossible. Thus, for applied problems, related to solving Fredholm integral equation of the second kind, it is expedient to use not mesh, but the projection and the projection-mesh randomized algorithms.",
keywords = "Fredholm integral equation of the second kind, numerical solution, randomized algorithms, projection, mesh, projection-mesh algorithms, important (actual) applied problems: computability of kernel and free term of an equation",
author = "Voytishek, {Anton V.} and Shipilov, {Nikolay M.}",
year = "2017",
month = nov,
day = "14",
doi = "10.1063/1.5012637",
language = "English",
volume = "1907",
series = "AIP Conference Proceedings",
publisher = "American Institute of Physics Inc.",
editor = "IE Egorov and SV Popov and PN Vabishchevich and MY Antonov and NP Lazarev and MS Troeva and MS Troeva and AO Ivanova and YM Grigorev",
booktitle = "Proceedings of the 8th International Conference on Mathematical Modeling, ICMM 2017",
note = "8th International Conference on Mathematical Modeling, ICMM 2017 ; Conference date: 04-07-2017 Through 08-07-2017",

}

RIS

TY - GEN

T1 - On randomized algorithms for numerical solution of applied Fredholm integral equations of the second kind

AU - Voytishek, Anton V.

AU - Shipilov, Nikolay M.

PY - 2017/11/14

Y1 - 2017/11/14

N2 - In this paper, the systematization of numerical (implemented on a computer) randomized functional algorithms for approximation of a solution of Fredholm integral equation of the second kind is carried out. Wherein, three types of such algorithms are distinguished: the projection, the mesh and the projection-mesh methods. The possibilities for usage of these algorithms for solution of practically important problems is investigated in detail. The disadvantages of the mesh algorithms, related to the necessity of calculation values of the kernels of integral equations in fixed points, are identified. On practice, these kernels have integrated singularities, and calculation of their values is impossible. Thus, for applied problems, related to solving Fredholm integral equation of the second kind, it is expedient to use not mesh, but the projection and the projection-mesh randomized algorithms.

AB - In this paper, the systematization of numerical (implemented on a computer) randomized functional algorithms for approximation of a solution of Fredholm integral equation of the second kind is carried out. Wherein, three types of such algorithms are distinguished: the projection, the mesh and the projection-mesh methods. The possibilities for usage of these algorithms for solution of practically important problems is investigated in detail. The disadvantages of the mesh algorithms, related to the necessity of calculation values of the kernels of integral equations in fixed points, are identified. On practice, these kernels have integrated singularities, and calculation of their values is impossible. Thus, for applied problems, related to solving Fredholm integral equation of the second kind, it is expedient to use not mesh, but the projection and the projection-mesh randomized algorithms.

KW - Fredholm integral equation of the second kind

KW - numerical solution

KW - randomized algorithms

KW - projection

KW - mesh

KW - projection-mesh algorithms

KW - important (actual) applied problems: computability of kernel and free term of an equation

UR - http://www.scopus.com/inward/record.url?scp=85036555981&partnerID=8YFLogxK

U2 - 10.1063/1.5012637

DO - 10.1063/1.5012637

M3 - Conference contribution

AN - SCOPUS:85036555981

VL - 1907

T3 - AIP Conference Proceedings

BT - Proceedings of the 8th International Conference on Mathematical Modeling, ICMM 2017

A2 - Egorov, IE

A2 - Popov, SV

A2 - Vabishchevich, PN

A2 - Antonov, MY

A2 - Lazarev, NP

A2 - Troeva, MS

A2 - Troeva, MS

A2 - Ivanova, AO

A2 - Grigorev, YM

PB - American Institute of Physics Inc.

T2 - 8th International Conference on Mathematical Modeling, ICMM 2017

Y2 - 4 July 2017 through 8 July 2017

ER -

ID: 9648148