I. I. Kolotov, D. V. Lukyanenko, I. É. Stepanova, A. G. Yagola, “On the uniqueness of solutions to systems of linear algebraic equations resulting from the reduction of linear inverse problems of gravimetry and magnetometry: a local case”, Zh. Vychisl. Mat. Mat. Fiz., 2023, Volume 63, Number 8,Pages <nobr>1317

This article is cited in 7 papers

Partial Differential Equations

On the uniqueness of solutions to systems of linear algebraic equations resulting from the reduction of linear inverse problems of gravimetry and magnetometry: a local case

I. I. Kolotov^a, D. V. Lukyanenko^a, I. É. Stepanova^ab, A. G. Yagola^a

^a Faculty of Physics, Lomonosov Moscow State University, 119992, Moscow, Russia
^b Schmidt Institute of Physics of the Earth, Russian Academy of Sciences, 123995, Moscow, Russia

Abstract: The paper considers issues of unique solvability of systems of linear algebraic equations to which many inverse problems of geophysics are reduced as a result of discretization. Examples of degenerate and nondegenerate systems of different dimensions arising from the interpretation of gravity and magnetometric data are given.

Key words: degenerate systems of linear algebraic equations, integral representations, unique solvability.

UDC: 519.635

Received: 06.02.2023
Revised: 19.03.2023
Accepted: 28.04.2023

DOI: 10.31857/S0044466923080094