Nonlinear matrix algebra and engineering applications. Part 1: Theory and linear form matrix

摘要

A matrix vector formalism is developed for systematizing the manipulation of sets of non-linear algebraic equations. In this formalism all manipulations are performed by multiplication with specially constructed transformation matrices. For many important classes of nonlinearities, algorithms based on this formalism are presented for rearranging a set of equations so that their solution may be obtained by numerically searching along a single variable. Theory developed proves that all solutions are obtained.