Factored solution of nonlinear equation systems

Abstract

This article generalizes a recently introduced procedure to solve nonlinear systems of equations, radically departing from the conventional Newton–Raphson scheme. The original nonlinear system is first unfolded into three simpler components: (i) an underdetermined linear system, (ii) a one-to-one nonlinear mapping with explicit inverse, and (iii) an overdetermined linear system. Then, instead of solving such an augmented system at once, a two-step procedure is proposed in which two equation systems are solved at each iteration, one of them involving the same symmetric matrix throughout the solution process. The resulting factored algorithm converges faster than Newton's method and, if carefully implemented, can be computationally competitive for large-scale systems. It can also be advantageous for dealing with infeasible cases.