AMMAR BENDJABRI2021-11-072021-11-072021http://dspace.univ-msila.dz:8080//xmlui/handle/123456789/27261In 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 RA or in     ,  R A  R A respectively. Due to the nonclosed range RA 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.Article