On the influence of disturbances on the accuracy of computing corrections in the Krylov subspace

V. P. Il'in^a, V. N. Babenko<sup>b

a</sup> Institute of Computational Mathematics and Mathematical Geophysics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia
^b Kuban State Technological University, Krasnodar, 350072 Russia

Abstract: Rounding errors inevitably occur when performing calculations on a computer. In this paper, we study the impact of these errors on the accuracy of calculating the correction in the Krylov subspace. An estimate of the accuracy of the calculated correction, expressed via perturbations of the original data, is obtained.

Keywords: orthoprojector, Krylov subspace, projection method, Arnoldi orthogonalization, highdimensional SLAE, rounding error.

UDC: 519.61

Received: 26.10.2024
Revised: 12.04.2025
Accepted: 21.04.2025

DOI: 10.33048/SIBJIM.2025.28.101

 English version: Journal of Applied and Industrial Mathematics, 2025, 19:1, 51–58