In this work we concern with the approximate solution of the linear equation Af f where
A is injective and compact operator, this equation admits a unique solution in direct sense or in
the least square sense provided the right-hand side f is in RA or in , R A R A
respectively. Due to the nonclosed range RA the solution is not stable. Besides, if A is positive
de.nite we can replace the original equation by the auxiliary one A f where its
solution exist, stable and converges to the exact solution of the original equation as
tends to zero.