Algorithm for Solving Systems with Band Matrices in the Problems of Predicting the Service Life of Welded Structures

New efficient algorithmic and software tools for solving systems of linear algebraic equations of super large orders with an assessment of the reliability of the results obtained have been developed. The application of the developed algorithms is aimed at numerical prediction of the bearing capacity, residual life and serviceability of critical welded structures, in particular, main pipelines and pressure vessels with identified operational defects. The use of specialized computational methods not only improves the accuracy of residual life estimation, but also optimizes the processes of technical diagnostics and life extension of critical engineering facilities