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

被引：0

作者：

Voytishek A.V. ^{[1
,2
]}

机构：

[1] Institute of Computational Mathematics and Mathematical Geophysics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk

[2] Novosibirsk State University, Novosibirsk

来源：

Journal of Mathematical Sciences | 2021年 / 254卷 / 5期

关键词：

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

D O I：

10.1007/s10958-021-05328-z

中图分类号：

学科分类号：

摘要：

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. © 2021, Springer Science+Business Media, LLC, part of Springer Nature.

引用

页码：589 / 605

页数：16

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