## 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.

Original language | English |
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Pages (from-to) | 589-605 |

Number of pages | 17 |

Journal | Journal of Mathematical Sciences (United States) |

Volume | 254 |

Issue number | 5 |

DOIs | |

Publication status | Published - May 2021 |

## Keywords

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

## OECD FOS+WOS

- 1.01 MATHEMATICS
- 1.01.XY STATISTICS & PROBABILITY
- 1.01.PN MATHEMATICS, APPLIED