On the Solution of a Class of Nonlinear Systems Governed by an M-Matrix

الملخص EN

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.