When an infinite dimensional nonlinear equation is to be solved using a computer, the numerical analyst must decide either to discretize it first and thus to preserve and to transfer the nonlinear aspect to some finite dimensional space, or to linearize it first and then discretize the linear problem. The authors of this work have studied both possibilities and have proved the advantages of the second option. The talk will show, from a mathematical standpoint, why the approximate solution obtained by linearizing first and discretizing after, is more accurate than the one produced when proceeding in the inverse order. Applications to Fredholm integral equations of the second kind and to differential spectral problems will illustrate the theoretical conclusions.