Step-by-step inversion method for elasticity problems

The paper presents a new efficient method for solving the difference problem in the domains of a standard shape for the elasticity problems (step-by-step inversion method) for two-dimensional case. $N^{3/2}$ arithmetic operations are required for obtaining a solution to the problem by this method, $N$ is the number of unknowns. It is greater than $N\ln(N)$ – the number of operations necessary to realize the conventional efficient direct methods for equations of the elliptic kind with separated variables (the fast Fourier transform, cyclic reduction technique). But it is considerable less than $N^3$ – the number of operations necessary to realize the Gauss type method for this problem.