We consider the issues associated with the creation of an intelligent computing environment for the high-performance solution of a wide class of large algebraic problems, which makes up the most resource-intensive stage of mathematical modeling. The first area of research is devoted to automating the construction of parallel algorithms and their mapping onto supercomputer architecture by investigating the problem of classification and identification of matrix statements and selecting algorithms for specific situations relying on optimization methods. The second aspect is related to the creation of intelligent interfaces, both for internal inter-module interactions and for end-users from various professional backgrounds. The rich functionality of the high-tech software under discussion requires an advanced system content to manage machine experiments. The scale of this development puts on the agenda the creation of an integrated tool environment or ecosystem, as well as the concept of a mathematical knowledge base.