The monograph discusses algorithms designed to study spectral problems with symmetric matrices on computers and solve arbitrary systems of linear equations. For the first time, an end-to-end analysis of the accumulation of computational errors was carried out. Algorithms are described, the results of which, along with the solution vector, are an estimate of its error and the number of conditions of the matrix of coefficients of the solved system. The book is intended for specialists in computational mathematics, engineers, teachers and university students.