Geodesic
Classification and applications of randomized functional numerical algorithms for the solution of second-kind Fredholm integral equations
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Mathematical Analysis, Tome 155 (2018), pp. 3-19

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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: second-kind Fredholm integral equation, numerical solution, randomized algorithm, projection algorithm, grid algorithm, computational kernel. 
@article{INTO_2018_155_a0,
     author = {A. V. Voitishek},
     title = {Classification and applications of randomized functional numerical algorithms for the solution of second-kind {Fredholm} integral equations},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {3--19},
     publisher = {mathdoc},
     volume = {155},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2018_155_a0/}
}
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A. V. Voitishek. Classification and applications of randomized functional numerical algorithms for the solution of second-kind Fredholm integral equations. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Mathematical Analysis, Tome 155 (2018), pp. 3-19. http://geodesic.mathdoc.fr/item/INTO_2018_155_a0/