Preconditioners for the Conjugate Gradient method are studied to solve the Newton
system with symmetric positive definite (SPD) Jacobian. Following a previous theoretical work in we start from a given approximation of the inverse of the initial Jacobian,
and we construct a sequence of preconditioners by means of a low rank update, for the linearized systems arising
in the Picard-Newton solution of the nonlinear discretized Richards equation.
Numerical results onto a very large and realistic test case show that the proposed approach is more efficient,
in terms of iteration number and CPU time, as compared to computing the preconditioner of choice at every nonlinear iteration.
