Application of the Richardson method in case of the unknown lower bound of a problem spectrum

An algorithm, which allows to use an iterative Richardson's method for solving a system of linear algebraic equations, with the matrix corresponding to a sign-definite self-adjoint operator, in case of the absence of information about the lower boundary of the spectrum of problem is presented. The algorithm is based on the simultaneous operation of the two competing processes, the effectiveness of which is constantly analyzed. The elements of linear algebra concerning the spectral estimates, which are necessary to understand the details of the Richardson method with Chebyshev set of parameters, are presented. The method is explained on the example of onedimensional equation of elliptic type.