On the Solution of a Class of Nonlinear Systems Governed by an M‐Matrix
Woula Themistoclakis, Antonia Vecchio · Discrete Dynamics in Nature and Society · 2012
We consider a weakly nonlinear system of the form (I + φ(x)A)x = p, where φ(x) is a real function of the unknown vector x, and (I + φ(x)A) is an M‐matrix. We propose to solve it by means of a sequence of linear systems defined by the iteration procedure (I + φ(xr)A)xr+1 = p, r = 0, 1, …. The global convergence is proved by considering a related fixed‐point problem.