ABSTRACT
By definition, a geometric sequence is the one whose differences of the successive terms are always equal to each other. There are many apparently different, but often mathematically equivalent methods for solving an inverse problem and most of them resort to a system of linear equations in some important computational stages of the analysis. The way of solving a system of linear equations via the Gauss–Seidel method and the like is no longer in routine use for extensive numerical purposes, due to their performance with comparatively low efficiency relative to the modern software of the lower-upper decomposition types. The exact iterative solution of a system of linear equations will be found within the Gauss–Seidel methodology in a versatile setting of the Schmidt relaxations.
