Mathematical modeling

On numerical methods for solving infinite systems of linear algebraic equations

F. M. Fedorov, O. F. Ivanova^a, N. N. Pavlov^a, S. V. Potapova<sup>b

a</sup> North-Eastern Federal University named after M. K. Ammosov, Yakutsk
^b Research Institute of Mathematics of North-Eastern Federal University named after M. K. Amosov

Abstract: Numerical methods for solving in nite systems of linear algebraic equations are considered. First, the Gauss-Jordan method is formally generalized to in nite systems. It is shown that, on the basis of such an algorithm, it is possible to formally generalize other numerical methods, for example, the method of successive approximations or the iterative Seidel method. Then, using examples of speci c joint in nite systems, the e ciency of these methods was tested. A numerical comparison of these methods is given.

Keywords: infinite systems, Gauss algorithm, Cramer’s determinant, Gaussian systems, quasi-infinite systems, reduction method in the narrow and broad senses.

UDC: 519.61

Received: 16.09.2021
Accepted: 31.05.2022

DOI: 10.25587/SVFU.2022.12.93.009