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

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 a...

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Vydáno v:Journal of mathematical sciences (New York, N.Y.) Ročník 254; číslo 5; s. 589 - 605
Hlavní autor: Voytishek, A. V.
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Springer US 01.05.2021
Springer
Springer Nature B.V
Témata:
Algorithms
Fredholm equations
Integral equations
Kernels
Mathematics
Mathematics and Statistics
Projection
numerical solution
65C40
grid algorithm
computational kernel
45B05
randomized algorithm
65C05
projection algorithm
second-kind Fredholm integral equation
ISSN:1072-3374, 1573-8795
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Shrnutí: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.
Bibliografie:ObjectType-Article-1
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content type line 14
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-021-05328-z