the method of 'external spiral for solving a large system of linear equations

Solving a linear system of n × n equations can be very difficult for the computer, especially if one needs the exact solution, even when the number n - of equations and of unknown variables is relatively small (a few thousands). all existing methods have to overcome at least one of the following problems: 1. computational complexity, which is expressed with the number of arithmetic operations required in order to determine a solution; 2. the possibility of overflow and underflow problems; 3. causing variations in the values of some coefficients in the initial system, which may be leading to instability of the solution; 4. requiring additional conditions for convergence; 5. in cases of a large number of equations and unknown variables it is often required that the systems matrix be: either sparse, or symmetrical, or diagonal, etc. this paper presents a method for solving a system of linear equations of arbitrary order (any number of equations and unknown variables) to which the problems listed above do not reflect.