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 11 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