  This paper presents an iterative method suitable for inverting semilinear
problems which are important kernels in many numerical applications. The
primary idea is to employ a parametrization that is able to reduce semilinear
problems into linear systems which are solvable using fast Poisson solvers.
Theoretical justifications are provided and supported by several experiments.
Numerical results show that the method is not only computationally less
expensive, but also yields accurate approximations.
