Goldscheider Method

The Goldsheider Method is one of many methods that are used to solve linear algebra problems. This method was developed by American mathematician John Goldsheider in 1954. It is used to find the inverse of a matrix, solve systems of linear equations, and other problems involving matrices and vectors.

The essence of Goldstein's method is that it is based on the properties of the determinant of the matrix and on the selection of elements using elementary transformations. The peculiarity of the method is to divide the matrix into blocks of matrices and sequentially apply elementary operations to them to calculate the determinants.

The main idea of ​​the Goldstein method is as follows: let a square matrix A of size NxN be given and have a determinant that is not equal to zero. Then we can divide the matrix into two blocks, each of size (N-1)

The study of the theory of elasticity comes down to the study of three main problems: direct and inverse problems of geometric optics; bends of straight and elastic lines; tensile and compressive stresses. The transition from the first of these problems to the other two is carried out using the Goldsteiner method.

Currently, the Goldstein Method is a generally accepted method for calculating VAT in international scientific practice. This is largely due to the mathematical rigor and simplicity of the calculation algorithm. In addition, it is quite universal, which means it is applicable to all types of calculations. The method is of particular interest when applied to conditions of static and dynamic loading. Obviously, we are talking about the time and costs required to determine the state of the material structure at a specific point in the cycle. The least labor-intensive step seems to be the stage of breaking the structure into elements and analyzing the stress-strain state of the local zone - this is exactly what is carried out by Goldstein.

Numerical example from mathematical theory. Guess