METHODS OF LINEAR ALGEBRA IN THE ANALYSIS OF CERTAIN CLASSES OF NONLINEAR DISCRETELY TRANSFORMATIVE SYSTEMS. I. MULTIPLICATIVE NONLINEAR SYSTEMS

摘要

The ideas and methods of pseudo-inversion of linear algebraic systems are propagated to problems of constructing the best root mean square approximation to solutions of nonlinear discretely transformative systems. The cases are considered where the form of nonlinearity is defined by a Cartesian product or iterative specification of linearly transformed input. Pseudo-solutions of quadratic nonlinear systems and systems of arbitrary order of nonlinearity are constructed and analyzed for accuracy and uniqueness.