Olexander N. Methods for the computer investigation of mathematical models with approximately given initial data.

The theoretical foundations are laid and the algorithms are created for computer-based investigation of and solution to mathematical problems with approximately given initial data, to which mathematical modelling of processes, phenomena and systems from various subject areas can be reduced, where solution to linear algebraic problems (linear algebraic systems and algebraic eigenvalue problem) is either an intermediate or a final stage. The principles of a creation of the intelligent software, intended for investigation of and solution to mathematical problems with approximately given initial data along with estimating a reliability of obtained results, are created. The investigation is carried out both for the computers with the traditional architecture and parallel MIMD-computers. The conceptual basis both of the methodology for the computer-based investigation of mathematical models with approximately given initial data and software intended for automatic solving of such problems is the correlated process: investigation of mathematical features of machine models of problems, creation of a method used to obtain an approximate solution depending on revealed characteristics of a machine model as well as machine solution reliability estimation. Key words: mathematical model, machine model, approximately given initial data, computer methods, error estimate, intelligent software, MIMD-computers, parallel computation algorithms.