Features of solutions of SLAE with functional coefficients

Abstract

The objective of this study is to determine the influence of functional relationships between the coefficients of the system of linear algebraic equations (SLAE) on the correctness of the solutions of the inverse linear magnetometry problem. The tasks of the study are the analysis of existing approaches to the formation of methods for solving SLAE, the determination of the areas of existence of stable solutions of the inverse linear magnetometry problem and of the directions of the development of SLAE solution methods. The object of research is inverse problems of magnetometry, which reduce to the SLAE solution with functional coefficients. The subject of research is the features of SLAE solutions with functional coefficients using different structures of grid-block models of geological arrays and corresponding software algorithms. The work analyzes, summarizes and systemizes research on the problem of using different models and software algorithms for them. The necessity of transition to the development of iterative methods for solving SLAE is singled out, and direct methods are recommended to be used only for single-layer models of the geological environment. To estimate the effectiveness of the methods created, a mean square residual of the magnetic field is used. The results of the study are planned to be used for geological interpretation of magnetic field maps at detailed survey sites in Kryvyi Rih and in some other regions of Ukraine.