I.N.Sinitsyn, V.I. Sinitsyn, E.R.Korepanov, V.V.Belousov, T.D.Konashenkova, N.N. Semendyaev, D.A. Basilashvili

The article opens the thematic cycle dedicated to software tools for analysis and synthesis of stochastic systems with high availability. Problems of software tools in MATLAB based on canonical expansions (CE) of scalar stochastic functions are considered. In section 1 the problem statement is given. Section 2 contains main definitions and general formulae for CE coordinate functions. In Section 3 general approach and two general methods of CE construction are presented. 6 CE algorithms for scalar stochastic functions in the fixed domain are discussed in sections 4 and 5. In section 6 five methods of CE construction based on CE of covariation function are given. Section 7 is dedicated to CE based on stochastic function series. CE Methods of analytical and statistical modeling and simulation are considered in section 8. In section 9 together with Appendices 1 and 2 basic practical problems of software tools design are given. Section 10 contains main conclusions.