Classification and Applications of Randomized Functional Numerical Algorithms for the Solution of Second-Kind Fredholm Integral Equations

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Classification and Applications of Randomized Functional Numerical Algorithms for the Solution of Second-Kind Fredholm Integral Equations. / Voytishek, A. V.

In: Journal of Mathematical Sciences (United States), Vol. 254, No. 5, 05.2021, p. 589-605.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{39516b6f6f634cb08999e23473cd7426,

title = "Classification and Applications of Randomized Functional Numerical Algorithms for the Solution of Second-Kind Fredholm Integral Equations",

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 = "45B05, 65C05, 65C40, computational kernel, grid algorithm, numerical solution, projection algorithm, randomized algorithm, second-kind Fredholm integral equation",

author = "Voytishek, {A. V.}",

year = "2021",

month = may,

doi = "10.1007/s10958-021-05328-z",

language = "English",

volume = "254",

pages = "589--605",

journal = "Journal of Mathematical Sciences (United States)",

issn = "1072-3374",

publisher = "Springer Nature",

number = "5",

}

RIS

TY - JOUR

T1 - Classification and Applications of Randomized Functional Numerical Algorithms for the Solution of Second-Kind Fredholm Integral Equations

AU - Voytishek, A. V.

PY - 2021/5

Y1 - 2021/5

N2 - 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.

AB - 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.

KW - 45B05

KW - 65C05

KW - 65C40

KW - computational kernel

KW - grid algorithm

KW - numerical solution

KW - projection algorithm

KW - randomized algorithm

KW - second-kind Fredholm integral equation

UR - http://www.scopus.com/inward/record.url?scp=85103406542&partnerID=8YFLogxK

U2 - 10.1007/s10958-021-05328-z

DO - 10.1007/s10958-021-05328-z

M3 - Article

AN - SCOPUS:85103406542

VL - 254

SP - 589

EP - 605

JO - Journal of Mathematical Sciences (United States)

JF - Journal of Mathematical Sciences (United States)

SN - 1072-3374

IS - 5

ER -

ID: 28255905