diff --git a/krylov/psb_base_krylov_conv_mod.f90 b/krylov/psb_base_krylov_conv_mod.f90
index a00b20c8..9eb1a366 100644
--- a/krylov/psb_base_krylov_conv_mod.f90
+++ b/krylov/psb_base_krylov_conv_mod.f90
@@ -42,8 +42,9 @@ Module psb_base_krylov_conv_mod
   end interface
 
   integer(psb_ipk_), parameter :: psb_ik_bni_=1, psb_ik_rni_=2, psb_ik_ani_=3
-  integer(psb_ipk_), parameter :: psb_ik_xni_=4, psb_ik_bn2_=5, psb_ik_xn2_=6
-  integer(psb_ipk_), parameter :: psb_ik_errnum_=7, psb_ik_errden_=8, psb_ik_eps_=9, psb_ik_rn2_=10
+  integer(psb_ipk_), parameter :: psb_ik_xni_=4, psb_ik_bn2_=5, psb_ik_r0n2_=6
+  integer(psb_ipk_), parameter :: psb_ik_xn2_=7, psb_ik_errnum_=8, psb_ik_errden_=9
+  integer(psb_ipk_), parameter :: psb_ik_eps_=10, psb_ik_rn2_=11
   integer(psb_ipk_), parameter :: psb_ik_stopc_=1, psb_ik_trace_=2, psb_ik_itmax_=3
   integer(psb_ipk_), parameter :: psb_ik_ivsz_=16
   type psb_itconv_type
diff --git a/krylov/psb_c_krylov_conv_mod.f90 b/krylov/psb_c_krylov_conv_mod.f90
index 632e84b7..fbca1cbb 100644
--- a/krylov/psb_c_krylov_conv_mod.f90
+++ b/krylov/psb_c_krylov_conv_mod.f90
@@ -48,13 +48,14 @@ Module psb_c_krylov_conv_mod
 
 contains
 
-  subroutine psb_c_init_conv(methdname,stopc,trace,itmax,a,b,eps,desc_a,stopdat,info)
+  subroutine psb_c_init_conv(methdname,stopc,trace,itmax,a,x,b,eps,&
+       & desc_a,stopdat,info)
     use psb_base_mod
     implicit none 
     character(len=*), intent(in)      :: methdname
     integer(psb_ipk_), intent(in)               :: stopc, trace, itmax
     type(psb_cspmat_type), intent(in) :: a
-    complex(psb_spk_), intent(in)     :: b(:)
+    complex(psb_spk_), intent(inout)     :: b(:), x(:)
     real(psb_spk_), intent(in)        :: eps
     type(psb_desc_type), intent(in)   :: desc_a
     type(psb_itconv_type)             :: stopdat
@@ -62,6 +63,7 @@ contains
 
     integer(psb_ipk_) :: ictxt, me, np, err_act, ierr(5)
     character(len=20)                 :: name
+    complex(psb_spk_), allocatable     :: r(:)
 
     info = psb_success_
     name = 'psb_init_conv'
@@ -88,6 +90,12 @@ contains
     case (2) 
       stopdat%values(psb_ik_bn2_) = psb_genrm2(b,desc_a,info)
 
+    case (3)
+      call psb_geall(r,desc_a,info)
+      call psb_geaxpby(cone,b,czero,r,desc_a,info)
+      call psb_spmm(-cone,a,x,cone,r,desc_a,info)
+      stopdat%values(psb_ik_r0n2_) = psb_genrm2(r,desc_a,info)
+      call psb_gefree(r,desc_a,info)
     case default
       info=psb_err_invalid_istop_
       ierr(1) = stopc
@@ -152,6 +160,11 @@ contains
       stopdat%values(psb_ik_errnum_) = stopdat%values(psb_ik_rn2_)
       stopdat%values(psb_ik_errden_) = stopdat%values(psb_ik_bn2_)
 
+    case(3)
+      stopdat%values(psb_ik_rn2_)  = psb_genrm2(r,desc_a,info)
+      stopdat%values(psb_ik_errnum_) = stopdat%values(psb_ik_rn2_)
+      stopdat%values(psb_ik_errden_) = stopdat%values(psb_ik_r0n2_)
+
     case default
       info=psb_err_internal_error_
       call psb_errpush(info,name,a_err="Control data in stopdat messed up!")
@@ -188,20 +201,21 @@ contains
   end function psb_c_check_conv
 
 
-  subroutine psb_c_init_conv_vect(methdname,stopc,trace,itmax,a,b,eps,desc_a,stopdat,info)
+  subroutine psb_c_init_conv_vect(methdname,stopc,trace,itmax,a,x,b,eps,desc_a,stopdat,info)
     use psb_base_mod
     implicit none 
     character(len=*), intent(in)      :: methdname
     integer(psb_ipk_), intent(in)               :: stopc, trace,itmax
     type(psb_cspmat_type), intent(in) :: a
     real(psb_spk_), intent(in)        :: eps
-    type(psb_c_vect_type), intent(inout)  :: b
+    type(psb_c_vect_type), intent(inout)  :: x, b
     type(psb_desc_type), intent(in)   :: desc_a
     type(psb_itconv_type)             :: stopdat
     integer(psb_ipk_), intent(out)              :: info
 
     integer(psb_ipk_) :: ictxt, me, np, err_act, ierr(5)
     character(len=20)                 :: name
+    type(psb_c_vect_type) :: r
 
     info = psb_success_
     name = 'psb_init_conv'
@@ -228,6 +242,12 @@ contains
     case (2) 
       stopdat%values(psb_ik_bn2_) = psb_genrm2(b,desc_a,info)
 
+    case (3)
+      call psb_geasb(r,desc_a,info,scratch=.true.)
+      call psb_geaxpby(cone,b,czero,r,desc_a,info)
+      call psb_spmm(-cone,a,x,cone,r,desc_a,info)
+      stopdat%values(psb_ik_r0n2_) = psb_genrm2(r,desc_a,info)
+      call psb_gefree(r,desc_a,info)
     case default
       info=psb_err_invalid_istop_
       ierr(1) = stopc
@@ -293,6 +313,11 @@ contains
       stopdat%values(psb_ik_errnum_) = stopdat%values(psb_ik_rn2_)
       stopdat%values(psb_ik_errden_) = stopdat%values(psb_ik_bn2_)
 
+    case(3)
+      stopdat%values(psb_ik_rn2_)  = psb_genrm2(r,desc_a,info)
+      stopdat%values(psb_ik_errnum_) = stopdat%values(psb_ik_rn2_)
+      stopdat%values(psb_ik_errden_) = stopdat%values(psb_ik_r0n2_)
+
     case default
       info=psb_err_internal_error_
       call psb_errpush(info,name,a_err="Control data in stopdat messed up!")
diff --git a/krylov/psb_cbicg.f90 b/krylov/psb_cbicg.f90
index d15674a8..12d91f66 100644
--- a/krylov/psb_cbicg.f90
+++ b/krylov/psb_cbicg.f90
@@ -226,7 +226,7 @@ subroutine psb_cbicg_vect(a,prec,b,x,eps,desc_a,info,&
   itx   = 0
 
 
-  call psb_init_conv(methdname,istop_,itrace_,itmax_,a,b,eps,desc_a,stopdat,info)
+  call psb_init_conv(methdname,istop_,itrace_,itmax_,a,x,b,eps,desc_a,stopdat,info)
   if (info /= psb_success_) Then 
      call psb_errpush(psb_err_from_subroutine_non_,name)
      goto 9999
diff --git a/krylov/psb_ccg.F90 b/krylov/psb_ccg.F90
index 07017652..c9787f82 100644
--- a/krylov/psb_ccg.F90
+++ b/krylov/psb_ccg.F90
@@ -222,7 +222,7 @@ subroutine psb_ccg_vect(a,prec,b,x,eps,desc_a,info,&
 
     rho = czero
     
-    call psb_init_conv(methdname,istop_,itrace_,itmax_,a,b,eps,desc_a,stopdat,info)
+    call psb_init_conv(methdname,istop_,itrace_,itmax_,a,x,b,eps,desc_a,stopdat,info)
     if (info /= psb_success_) Then 
       call psb_errpush(psb_err_from_subroutine_non_,name)
       goto 9999
diff --git a/krylov/psb_ccgs.f90 b/krylov/psb_ccgs.f90
index 0a52bc5f..1b35ef98 100644
--- a/krylov/psb_ccgs.f90
+++ b/krylov/psb_ccgs.f90
@@ -200,7 +200,7 @@ Subroutine psb_ccgs_vect(a,prec,b,x,eps,desc_a,info,&
 
   itx   = 0
 
-  call psb_init_conv(methdname,istop_,itrace_,itmax_,a,b,eps,desc_a,stopdat,info)
+  call psb_init_conv(methdname,istop_,itrace_,itmax_,a,x,b,eps,desc_a,stopdat,info)
   if (info /= psb_success_) Then 
      call psb_errpush(psb_err_from_subroutine_non_,name)
      goto 9999
diff --git a/krylov/psb_ccgstab.f90 b/krylov/psb_ccgstab.f90
index b5ae0f02..4834cf2e 100644
--- a/krylov/psb_ccgstab.f90
+++ b/krylov/psb_ccgstab.f90
@@ -215,7 +215,7 @@ Subroutine psb_ccgstab_vect(a,prec,b,x,eps,desc_a,info,itmax,iter,err,itrace,ist
   End If
 
   itx   = 0
-  call psb_init_conv(methdname,istop_,itrace_,itmax_,a,b,eps,desc_a,stopdat,info)
+  call psb_init_conv(methdname,istop_,itrace_,itmax_,a,x,b,eps,desc_a,stopdat,info)
   if (psb_errstatus_fatal()) Then 
     call psb_errpush(psb_err_from_subroutine_non_,name)
     goto 9999
diff --git a/krylov/psb_ccgstabl.f90 b/krylov/psb_ccgstabl.f90
index 9382e312..ca2bcd63 100644
--- a/krylov/psb_ccgstabl.f90
+++ b/krylov/psb_ccgstabl.f90
@@ -245,7 +245,7 @@ Subroutine psb_ccgstabl_vect(a,prec,b,x,eps,desc_a,info,&
   rt0 => wwrk(10)
   
 
-  call psb_init_conv(methdname,istop_,itrace_,itmax_,a,b,eps,desc_a,stopdat,info)
+  call psb_init_conv(methdname,istop_,itrace_,itmax_,a,x,b,eps,desc_a,stopdat,info)
   if (info /= psb_success_) Then 
      call psb_errpush(psb_err_from_subroutine_non_,name)
      goto 9999
diff --git a/krylov/psb_cfcg.F90 b/krylov/psb_cfcg.F90
index b47fb7e1..72ea8a60 100644
--- a/krylov/psb_cfcg.F90
+++ b/krylov/psb_cfcg.F90
@@ -209,7 +209,7 @@ subroutine psb_cfcg_vect(a,prec,b,x,eps,desc_a,info,&
        & scratch=.true.,mold=x%v)
 
 
-    call psb_init_conv(methdname,istop_,itrace_,itmax_,a,b,eps,desc_a,stopdat,info)
+    call psb_init_conv(methdname,istop_,itrace_,itmax_,a,x,b,eps,desc_a,stopdat,info)
   itx=0
 
   restart: do 
diff --git a/krylov/psb_cgcr.f90 b/krylov/psb_cgcr.f90
index 76dba4d6..933652fb 100644
--- a/krylov/psb_cgcr.f90
+++ b/krylov/psb_cgcr.f90
@@ -246,7 +246,7 @@ subroutine psb_cgcr_vect(a,prec,b,x,eps,desc_a,info,&
   itx = 0
   
   nrst = -1
-  call psb_init_conv(methdname,istop_,itrace_,itmax_,a,b,eps,desc_a,stopdat,info)
+  call psb_init_conv(methdname,istop_,itrace_,itmax_,a,x,b,eps,desc_a,stopdat,info)
   restart: do 
     if (itx>= itmax_) exit restart 
     h = czero
diff --git a/krylov/psb_crgmres.f90 b/krylov/psb_crgmres.f90
index 13875c1d..505f6609 100644
--- a/krylov/psb_crgmres.f90
+++ b/krylov/psb_crgmres.f90
@@ -137,7 +137,7 @@ subroutine psb_crgmres_vect(a,prec,b,x,eps,desc_a,info,&
   integer(psb_ipk_) :: itx, i, istop_, err_act
   integer(psb_ipk_) :: debug_level, debug_unit
   integer(psb_ipk_) :: ictxt, np, me  
-  Real(psb_spk_)     :: rni, xni, bni, ani,bn2, dt
+  Real(psb_spk_)     :: rni, xni, bni, ani,bn2, dt, r0n2
   real(psb_dpk_)     :: errnum, errden, deps, derr
   character(len=20)           :: name
   character(len=*), parameter :: methdname='RGMRES'
@@ -258,6 +258,21 @@ subroutine psb_crgmres_vect(a,prec,b,x,eps,desc_a,info,&
     bni = psb_geamax(b,desc_a,info)
   else if (istop_ == 2) then 
     bn2 = psb_genrm2(b,desc_a,info)
+  else if (istop_ == 3) then
+    call psb_geaxpby(cone,b,czero,v(1),desc_a,info)
+    if (info /= psb_success_) then 
+      info=psb_err_from_subroutine_non_ 
+      call psb_errpush(info,name)
+      goto 9999
+    end if
+    
+    call psb_spmm(-cone,a,x,cone,v(1),desc_a,info,work=aux)
+    if (info /= psb_success_) then 
+      info=psb_err_from_subroutine_non_ 
+      call psb_errpush(info,name)
+      goto 9999
+    end if
+    r0n2 = psb_genrm2(v(1),desc_a,info)
   endif
   errnum = czero
   errden = cone
@@ -274,7 +289,6 @@ subroutine psb_crgmres_vect(a,prec,b,x,eps,desc_a,info,&
   
     ! compute r0 = b-ax0
     ! check convergence
-    ! compute v1 = r0/||r0||_2
 
     if (debug_level >= psb_debug_ext_) &
          & write(debug_unit,*) me,' ',trim(name),&
@@ -319,6 +333,10 @@ subroutine psb_crgmres_vect(a,prec,b,x,eps,desc_a,info,&
       rni = psb_genrm2(v(1),desc_a,info)
       errnum = rni
       errden = bn2
+    else if (istop_ == 3) then 
+      rni = psb_genrm2(v(1),desc_a,info)
+      errnum = rni
+      errden = r0n2
     endif
     if (info /= psb_success_) then 
       info=psb_err_from_subroutine_non_ 
@@ -397,6 +415,14 @@ subroutine psb_crgmres_vect(a,prec,b,x,eps,desc_a,info,&
         rni = abs(rs(i+1))
         errnum = rni
         errden = bn2
+      else if (istop_ == 3) then 
+        !
+        ! compute the residual 2-norm as byproduct of the solution
+        ! procedure of the least-squares problem
+        !
+        rni = abs(rs(i+1))
+        errnum = rni
+        errden = r0n2
       endif
 
       if (errnum <= eps*errden) then 
diff --git a/krylov/psb_d_krylov_conv_mod.f90 b/krylov/psb_d_krylov_conv_mod.f90
index 2f839f7a..1a28f0a8 100644
--- a/krylov/psb_d_krylov_conv_mod.f90
+++ b/krylov/psb_d_krylov_conv_mod.f90
@@ -48,13 +48,14 @@ Module psb_d_krylov_conv_mod
 
 contains
 
-  subroutine psb_d_init_conv(methdname,stopc,trace,itmax,a,b,eps,desc_a,stopdat,info)
+  subroutine psb_d_init_conv(methdname,stopc,trace,itmax,a,x,b,eps,&
+       & desc_a,stopdat,info)
     use psb_base_mod
     implicit none 
     character(len=*), intent(in)      :: methdname
     integer(psb_ipk_), intent(in)               :: stopc, trace, itmax
     type(psb_dspmat_type), intent(in) :: a
-    real(psb_dpk_), intent(in)     :: b(:)
+    real(psb_dpk_), intent(inout)     :: b(:), x(:)
     real(psb_dpk_), intent(in)        :: eps
     type(psb_desc_type), intent(in)   :: desc_a
     type(psb_itconv_type)             :: stopdat
@@ -62,6 +63,7 @@ contains
 
     integer(psb_ipk_) :: ictxt, me, np, err_act, ierr(5)
     character(len=20)                 :: name
+    real(psb_dpk_), allocatable     :: r(:)
 
     info = psb_success_
     name = 'psb_init_conv'
@@ -88,6 +90,12 @@ contains
     case (2) 
       stopdat%values(psb_ik_bn2_) = psb_genrm2(b,desc_a,info)
 
+    case (3)
+      call psb_geall(r,desc_a,info)
+      call psb_geaxpby(done,b,dzero,r,desc_a,info)
+      call psb_spmm(-done,a,x,done,r,desc_a,info)
+      stopdat%values(psb_ik_r0n2_) = psb_genrm2(r,desc_a,info)
+      call psb_gefree(r,desc_a,info)
     case default
       info=psb_err_invalid_istop_
       ierr(1) = stopc
@@ -152,6 +160,11 @@ contains
       stopdat%values(psb_ik_errnum_) = stopdat%values(psb_ik_rn2_)
       stopdat%values(psb_ik_errden_) = stopdat%values(psb_ik_bn2_)
 
+    case(3)
+      stopdat%values(psb_ik_rn2_)  = psb_genrm2(r,desc_a,info)
+      stopdat%values(psb_ik_errnum_) = stopdat%values(psb_ik_rn2_)
+      stopdat%values(psb_ik_errden_) = stopdat%values(psb_ik_r0n2_)
+
     case default
       info=psb_err_internal_error_
       call psb_errpush(info,name,a_err="Control data in stopdat messed up!")
@@ -188,20 +201,21 @@ contains
   end function psb_d_check_conv
 
 
-  subroutine psb_d_init_conv_vect(methdname,stopc,trace,itmax,a,b,eps,desc_a,stopdat,info)
+  subroutine psb_d_init_conv_vect(methdname,stopc,trace,itmax,a,x,b,eps,desc_a,stopdat,info)
     use psb_base_mod
     implicit none 
     character(len=*), intent(in)      :: methdname
     integer(psb_ipk_), intent(in)               :: stopc, trace,itmax
     type(psb_dspmat_type), intent(in) :: a
     real(psb_dpk_), intent(in)        :: eps
-    type(psb_d_vect_type), intent(inout)  :: b
+    type(psb_d_vect_type), intent(inout)  :: x, b
     type(psb_desc_type), intent(in)   :: desc_a
     type(psb_itconv_type)             :: stopdat
     integer(psb_ipk_), intent(out)              :: info
 
     integer(psb_ipk_) :: ictxt, me, np, err_act, ierr(5)
     character(len=20)                 :: name
+    type(psb_d_vect_type) :: r
 
     info = psb_success_
     name = 'psb_init_conv'
@@ -228,6 +242,12 @@ contains
     case (2) 
       stopdat%values(psb_ik_bn2_) = psb_genrm2(b,desc_a,info)
 
+    case (3)
+      call psb_geasb(r,desc_a,info,scratch=.true.)
+      call psb_geaxpby(done,b,dzero,r,desc_a,info)
+      call psb_spmm(-done,a,x,done,r,desc_a,info)
+      stopdat%values(psb_ik_r0n2_) = psb_genrm2(r,desc_a,info)
+      call psb_gefree(r,desc_a,info)
     case default
       info=psb_err_invalid_istop_
       ierr(1) = stopc
@@ -293,6 +313,11 @@ contains
       stopdat%values(psb_ik_errnum_) = stopdat%values(psb_ik_rn2_)
       stopdat%values(psb_ik_errden_) = stopdat%values(psb_ik_bn2_)
 
+    case(3)
+      stopdat%values(psb_ik_rn2_)  = psb_genrm2(r,desc_a,info)
+      stopdat%values(psb_ik_errnum_) = stopdat%values(psb_ik_rn2_)
+      stopdat%values(psb_ik_errden_) = stopdat%values(psb_ik_r0n2_)
+
     case default
       info=psb_err_internal_error_
       call psb_errpush(info,name,a_err="Control data in stopdat messed up!")
diff --git a/krylov/psb_dbicg.f90 b/krylov/psb_dbicg.f90
index a347ddf1..55133945 100644
--- a/krylov/psb_dbicg.f90
+++ b/krylov/psb_dbicg.f90
@@ -226,7 +226,7 @@ subroutine psb_dbicg_vect(a,prec,b,x,eps,desc_a,info,&
   itx   = 0
 
 
-  call psb_init_conv(methdname,istop_,itrace_,itmax_,a,b,eps,desc_a,stopdat,info)
+  call psb_init_conv(methdname,istop_,itrace_,itmax_,a,x,b,eps,desc_a,stopdat,info)
   if (info /= psb_success_) Then 
      call psb_errpush(psb_err_from_subroutine_non_,name)
      goto 9999
diff --git a/krylov/psb_dcg.F90 b/krylov/psb_dcg.F90
index d42ff2bf..152293f6 100644
--- a/krylov/psb_dcg.F90
+++ b/krylov/psb_dcg.F90
@@ -230,7 +230,7 @@ subroutine psb_dcg_vect(a,prec,b,x,eps,desc_a,info,&
 
     rho = dzero
     
-    call psb_init_conv(methdname,istop_,itrace_,itmax_,a,b,eps,desc_a,stopdat,info)
+    call psb_init_conv(methdname,istop_,itrace_,itmax_,a,x,b,eps,desc_a,stopdat,info)
     if (info /= psb_success_) Then 
       call psb_errpush(psb_err_from_subroutine_non_,name)
       goto 9999
diff --git a/krylov/psb_dcgs.f90 b/krylov/psb_dcgs.f90
index 83b8c4a7..675c0881 100644
--- a/krylov/psb_dcgs.f90
+++ b/krylov/psb_dcgs.f90
@@ -200,7 +200,7 @@ Subroutine psb_dcgs_vect(a,prec,b,x,eps,desc_a,info,&
 
   itx   = 0
 
-  call psb_init_conv(methdname,istop_,itrace_,itmax_,a,b,eps,desc_a,stopdat,info)
+  call psb_init_conv(methdname,istop_,itrace_,itmax_,a,x,b,eps,desc_a,stopdat,info)
   if (info /= psb_success_) Then 
      call psb_errpush(psb_err_from_subroutine_non_,name)
      goto 9999
diff --git a/krylov/psb_dcgstab.f90 b/krylov/psb_dcgstab.f90
index 272b2f07..5c879cd7 100644
--- a/krylov/psb_dcgstab.f90
+++ b/krylov/psb_dcgstab.f90
@@ -215,7 +215,7 @@ Subroutine psb_dcgstab_vect(a,prec,b,x,eps,desc_a,info,itmax,iter,err,itrace,ist
   End If
 
   itx   = 0
-  call psb_init_conv(methdname,istop_,itrace_,itmax_,a,b,eps,desc_a,stopdat,info)
+  call psb_init_conv(methdname,istop_,itrace_,itmax_,a,x,b,eps,desc_a,stopdat,info)
   if (psb_errstatus_fatal()) Then 
     call psb_errpush(psb_err_from_subroutine_non_,name)
     goto 9999
diff --git a/krylov/psb_dcgstabl.f90 b/krylov/psb_dcgstabl.f90
index 738ef03f..b45811bc 100644
--- a/krylov/psb_dcgstabl.f90
+++ b/krylov/psb_dcgstabl.f90
@@ -245,7 +245,7 @@ Subroutine psb_dcgstabl_vect(a,prec,b,x,eps,desc_a,info,&
   rt0 => wwrk(10)
   
 
-  call psb_init_conv(methdname,istop_,itrace_,itmax_,a,b,eps,desc_a,stopdat,info)
+  call psb_init_conv(methdname,istop_,itrace_,itmax_,a,x,b,eps,desc_a,stopdat,info)
   if (info /= psb_success_) Then 
      call psb_errpush(psb_err_from_subroutine_non_,name)
      goto 9999
diff --git a/krylov/psb_dfcg.F90 b/krylov/psb_dfcg.F90
index a6456327..b3d8d0b3 100644
--- a/krylov/psb_dfcg.F90
+++ b/krylov/psb_dfcg.F90
@@ -209,7 +209,7 @@ subroutine psb_dfcg_vect(a,prec,b,x,eps,desc_a,info,&
        & scratch=.true.,mold=x%v)
 
 
-    call psb_init_conv(methdname,istop_,itrace_,itmax_,a,b,eps,desc_a,stopdat,info)
+    call psb_init_conv(methdname,istop_,itrace_,itmax_,a,x,b,eps,desc_a,stopdat,info)
   itx=0
 
   restart: do 
diff --git a/krylov/psb_dgcr.f90 b/krylov/psb_dgcr.f90
index 4a6c0e19..3c9c83f5 100644
--- a/krylov/psb_dgcr.f90
+++ b/krylov/psb_dgcr.f90
@@ -246,7 +246,7 @@ subroutine psb_dgcr_vect(a,prec,b,x,eps,desc_a,info,&
   itx = 0
   
   nrst = -1
-  call psb_init_conv(methdname,istop_,itrace_,itmax_,a,b,eps,desc_a,stopdat,info)
+  call psb_init_conv(methdname,istop_,itrace_,itmax_,a,x,b,eps,desc_a,stopdat,info)
   restart: do 
     if (itx>= itmax_) exit restart 
     h = dzero
diff --git a/krylov/psb_drgmres.f90 b/krylov/psb_drgmres.f90
index 1aa2b1f2..27a62ed9 100644
--- a/krylov/psb_drgmres.f90
+++ b/krylov/psb_drgmres.f90
@@ -137,7 +137,7 @@ subroutine psb_drgmres_vect(a,prec,b,x,eps,desc_a,info,&
   integer(psb_ipk_) :: itx, i, istop_, err_act
   integer(psb_ipk_) :: debug_level, debug_unit
   integer(psb_ipk_) :: ictxt, np, me  
-  Real(psb_dpk_)     :: rni, xni, bni, ani,bn2, dt
+  Real(psb_dpk_)     :: rni, xni, bni, ani,bn2, dt, r0n2
   real(psb_dpk_)     :: errnum, errden, deps, derr
   character(len=20)           :: name
   character(len=*), parameter :: methdname='RGMRES'
@@ -258,6 +258,21 @@ subroutine psb_drgmres_vect(a,prec,b,x,eps,desc_a,info,&
     bni = psb_geamax(b,desc_a,info)
   else if (istop_ == 2) then 
     bn2 = psb_genrm2(b,desc_a,info)
+  else if (istop_ == 3) then
+    call psb_geaxpby(done,b,dzero,v(1),desc_a,info)
+    if (info /= psb_success_) then 
+      info=psb_err_from_subroutine_non_ 
+      call psb_errpush(info,name)
+      goto 9999
+    end if
+    
+    call psb_spmm(-done,a,x,done,v(1),desc_a,info,work=aux)
+    if (info /= psb_success_) then 
+      info=psb_err_from_subroutine_non_ 
+      call psb_errpush(info,name)
+      goto 9999
+    end if
+    r0n2 = psb_genrm2(v(1),desc_a,info)
   endif
   errnum = dzero
   errden = done
@@ -274,7 +289,6 @@ subroutine psb_drgmres_vect(a,prec,b,x,eps,desc_a,info,&
   
     ! compute r0 = b-ax0
     ! check convergence
-    ! compute v1 = r0/||r0||_2
 
     if (debug_level >= psb_debug_ext_) &
          & write(debug_unit,*) me,' ',trim(name),&
@@ -319,6 +333,10 @@ subroutine psb_drgmres_vect(a,prec,b,x,eps,desc_a,info,&
       rni = psb_genrm2(v(1),desc_a,info)
       errnum = rni
       errden = bn2
+    else if (istop_ == 3) then 
+      rni = psb_genrm2(v(1),desc_a,info)
+      errnum = rni
+      errden = r0n2
     endif
     if (info /= psb_success_) then 
       info=psb_err_from_subroutine_non_ 
@@ -397,6 +415,14 @@ subroutine psb_drgmres_vect(a,prec,b,x,eps,desc_a,info,&
         rni = abs(rs(i+1))
         errnum = rni
         errden = bn2
+      else if (istop_ == 3) then 
+        !
+        ! compute the residual 2-norm as byproduct of the solution
+        ! procedure of the least-squares problem
+        !
+        rni = abs(rs(i+1))
+        errnum = rni
+        errden = r0n2
       endif
 
       if (errnum <= eps*errden) then 
diff --git a/krylov/psb_s_krylov_conv_mod.f90 b/krylov/psb_s_krylov_conv_mod.f90
index daff12ed..aac4736f 100644
--- a/krylov/psb_s_krylov_conv_mod.f90
+++ b/krylov/psb_s_krylov_conv_mod.f90
@@ -48,13 +48,14 @@ Module psb_s_krylov_conv_mod
 
 contains
 
-  subroutine psb_s_init_conv(methdname,stopc,trace,itmax,a,b,eps,desc_a,stopdat,info)
+  subroutine psb_s_init_conv(methdname,stopc,trace,itmax,a,x,b,eps,&
+       & desc_a,stopdat,info)
     use psb_base_mod
     implicit none 
     character(len=*), intent(in)      :: methdname
     integer(psb_ipk_), intent(in)               :: stopc, trace, itmax
     type(psb_sspmat_type), intent(in) :: a
-    real(psb_spk_), intent(in)     :: b(:)
+    real(psb_spk_), intent(inout)     :: b(:), x(:)
     real(psb_spk_), intent(in)        :: eps
     type(psb_desc_type), intent(in)   :: desc_a
     type(psb_itconv_type)             :: stopdat
@@ -62,6 +63,7 @@ contains
 
     integer(psb_ipk_) :: ictxt, me, np, err_act, ierr(5)
     character(len=20)                 :: name
+    real(psb_spk_), allocatable     :: r(:)
 
     info = psb_success_
     name = 'psb_init_conv'
@@ -88,6 +90,12 @@ contains
     case (2) 
       stopdat%values(psb_ik_bn2_) = psb_genrm2(b,desc_a,info)
 
+    case (3)
+      call psb_geall(r,desc_a,info)
+      call psb_geaxpby(sone,b,szero,r,desc_a,info)
+      call psb_spmm(-sone,a,x,sone,r,desc_a,info)
+      stopdat%values(psb_ik_r0n2_) = psb_genrm2(r,desc_a,info)
+      call psb_gefree(r,desc_a,info)
     case default
       info=psb_err_invalid_istop_
       ierr(1) = stopc
@@ -152,6 +160,11 @@ contains
       stopdat%values(psb_ik_errnum_) = stopdat%values(psb_ik_rn2_)
       stopdat%values(psb_ik_errden_) = stopdat%values(psb_ik_bn2_)
 
+    case(3)
+      stopdat%values(psb_ik_rn2_)  = psb_genrm2(r,desc_a,info)
+      stopdat%values(psb_ik_errnum_) = stopdat%values(psb_ik_rn2_)
+      stopdat%values(psb_ik_errden_) = stopdat%values(psb_ik_r0n2_)
+
     case default
       info=psb_err_internal_error_
       call psb_errpush(info,name,a_err="Control data in stopdat messed up!")
@@ -188,20 +201,21 @@ contains
   end function psb_s_check_conv
 
 
-  subroutine psb_s_init_conv_vect(methdname,stopc,trace,itmax,a,b,eps,desc_a,stopdat,info)
+  subroutine psb_s_init_conv_vect(methdname,stopc,trace,itmax,a,x,b,eps,desc_a,stopdat,info)
     use psb_base_mod
     implicit none 
     character(len=*), intent(in)      :: methdname
     integer(psb_ipk_), intent(in)               :: stopc, trace,itmax
     type(psb_sspmat_type), intent(in) :: a
     real(psb_spk_), intent(in)        :: eps
-    type(psb_s_vect_type), intent(inout)  :: b
+    type(psb_s_vect_type), intent(inout)  :: x, b
     type(psb_desc_type), intent(in)   :: desc_a
     type(psb_itconv_type)             :: stopdat
     integer(psb_ipk_), intent(out)              :: info
 
     integer(psb_ipk_) :: ictxt, me, np, err_act, ierr(5)
     character(len=20)                 :: name
+    type(psb_s_vect_type) :: r
 
     info = psb_success_
     name = 'psb_init_conv'
@@ -228,6 +242,12 @@ contains
     case (2) 
       stopdat%values(psb_ik_bn2_) = psb_genrm2(b,desc_a,info)
 
+    case (3)
+      call psb_geasb(r,desc_a,info,scratch=.true.)
+      call psb_geaxpby(sone,b,szero,r,desc_a,info)
+      call psb_spmm(-sone,a,x,sone,r,desc_a,info)
+      stopdat%values(psb_ik_r0n2_) = psb_genrm2(r,desc_a,info)
+      call psb_gefree(r,desc_a,info)
     case default
       info=psb_err_invalid_istop_
       ierr(1) = stopc
@@ -293,6 +313,11 @@ contains
       stopdat%values(psb_ik_errnum_) = stopdat%values(psb_ik_rn2_)
       stopdat%values(psb_ik_errden_) = stopdat%values(psb_ik_bn2_)
 
+    case(3)
+      stopdat%values(psb_ik_rn2_)  = psb_genrm2(r,desc_a,info)
+      stopdat%values(psb_ik_errnum_) = stopdat%values(psb_ik_rn2_)
+      stopdat%values(psb_ik_errden_) = stopdat%values(psb_ik_r0n2_)
+
     case default
       info=psb_err_internal_error_
       call psb_errpush(info,name,a_err="Control data in stopdat messed up!")
diff --git a/krylov/psb_sbicg.f90 b/krylov/psb_sbicg.f90
index b47b463e..3f6470af 100644
--- a/krylov/psb_sbicg.f90
+++ b/krylov/psb_sbicg.f90
@@ -226,7 +226,7 @@ subroutine psb_sbicg_vect(a,prec,b,x,eps,desc_a,info,&
   itx   = 0
 
 
-  call psb_init_conv(methdname,istop_,itrace_,itmax_,a,b,eps,desc_a,stopdat,info)
+  call psb_init_conv(methdname,istop_,itrace_,itmax_,a,x,b,eps,desc_a,stopdat,info)
   if (info /= psb_success_) Then 
      call psb_errpush(psb_err_from_subroutine_non_,name)
      goto 9999
diff --git a/krylov/psb_scg.F90 b/krylov/psb_scg.F90
index 74e2b6dd..2bee8573 100644
--- a/krylov/psb_scg.F90
+++ b/krylov/psb_scg.F90
@@ -230,7 +230,7 @@ subroutine psb_scg_vect(a,prec,b,x,eps,desc_a,info,&
 
     rho = szero
     
-    call psb_init_conv(methdname,istop_,itrace_,itmax_,a,b,eps,desc_a,stopdat,info)
+    call psb_init_conv(methdname,istop_,itrace_,itmax_,a,x,b,eps,desc_a,stopdat,info)
     if (info /= psb_success_) Then 
       call psb_errpush(psb_err_from_subroutine_non_,name)
       goto 9999
diff --git a/krylov/psb_scgs.f90 b/krylov/psb_scgs.f90
index 9a566a44..64f11ee0 100644
--- a/krylov/psb_scgs.f90
+++ b/krylov/psb_scgs.f90
@@ -200,7 +200,7 @@ Subroutine psb_scgs_vect(a,prec,b,x,eps,desc_a,info,&
 
   itx   = 0
 
-  call psb_init_conv(methdname,istop_,itrace_,itmax_,a,b,eps,desc_a,stopdat,info)
+  call psb_init_conv(methdname,istop_,itrace_,itmax_,a,x,b,eps,desc_a,stopdat,info)
   if (info /= psb_success_) Then 
      call psb_errpush(psb_err_from_subroutine_non_,name)
      goto 9999
diff --git a/krylov/psb_scgstab.f90 b/krylov/psb_scgstab.f90
index d1a4ff81..30c0e4c9 100644
--- a/krylov/psb_scgstab.f90
+++ b/krylov/psb_scgstab.f90
@@ -215,7 +215,7 @@ Subroutine psb_scgstab_vect(a,prec,b,x,eps,desc_a,info,itmax,iter,err,itrace,ist
   End If
 
   itx   = 0
-  call psb_init_conv(methdname,istop_,itrace_,itmax_,a,b,eps,desc_a,stopdat,info)
+  call psb_init_conv(methdname,istop_,itrace_,itmax_,a,x,b,eps,desc_a,stopdat,info)
   if (psb_errstatus_fatal()) Then 
     call psb_errpush(psb_err_from_subroutine_non_,name)
     goto 9999
diff --git a/krylov/psb_scgstabl.f90 b/krylov/psb_scgstabl.f90
index f3d65ea3..99c675f6 100644
--- a/krylov/psb_scgstabl.f90
+++ b/krylov/psb_scgstabl.f90
@@ -245,7 +245,7 @@ Subroutine psb_scgstabl_vect(a,prec,b,x,eps,desc_a,info,&
   rt0 => wwrk(10)
   
 
-  call psb_init_conv(methdname,istop_,itrace_,itmax_,a,b,eps,desc_a,stopdat,info)
+  call psb_init_conv(methdname,istop_,itrace_,itmax_,a,x,b,eps,desc_a,stopdat,info)
   if (info /= psb_success_) Then 
      call psb_errpush(psb_err_from_subroutine_non_,name)
      goto 9999
diff --git a/krylov/psb_sfcg.F90 b/krylov/psb_sfcg.F90
index 78dba287..8109e46f 100644
--- a/krylov/psb_sfcg.F90
+++ b/krylov/psb_sfcg.F90
@@ -209,7 +209,7 @@ subroutine psb_sfcg_vect(a,prec,b,x,eps,desc_a,info,&
        & scratch=.true.,mold=x%v)
 
 
-    call psb_init_conv(methdname,istop_,itrace_,itmax_,a,b,eps,desc_a,stopdat,info)
+    call psb_init_conv(methdname,istop_,itrace_,itmax_,a,x,b,eps,desc_a,stopdat,info)
   itx=0
 
   restart: do 
diff --git a/krylov/psb_sgcr.f90 b/krylov/psb_sgcr.f90
index d1a7ec9c..22e3bdad 100644
--- a/krylov/psb_sgcr.f90
+++ b/krylov/psb_sgcr.f90
@@ -246,7 +246,7 @@ subroutine psb_sgcr_vect(a,prec,b,x,eps,desc_a,info,&
   itx = 0
   
   nrst = -1
-  call psb_init_conv(methdname,istop_,itrace_,itmax_,a,b,eps,desc_a,stopdat,info)
+  call psb_init_conv(methdname,istop_,itrace_,itmax_,a,x,b,eps,desc_a,stopdat,info)
   restart: do 
     if (itx>= itmax_) exit restart 
     h = szero
diff --git a/krylov/psb_srgmres.f90 b/krylov/psb_srgmres.f90
index 1d30b744..5bfb0cfd 100644
--- a/krylov/psb_srgmres.f90
+++ b/krylov/psb_srgmres.f90
@@ -137,7 +137,7 @@ subroutine psb_srgmres_vect(a,prec,b,x,eps,desc_a,info,&
   integer(psb_ipk_) :: itx, i, istop_, err_act
   integer(psb_ipk_) :: debug_level, debug_unit
   integer(psb_ipk_) :: ictxt, np, me  
-  Real(psb_spk_)     :: rni, xni, bni, ani,bn2, dt
+  Real(psb_spk_)     :: rni, xni, bni, ani,bn2, dt, r0n2
   real(psb_dpk_)     :: errnum, errden, deps, derr
   character(len=20)           :: name
   character(len=*), parameter :: methdname='RGMRES'
@@ -258,6 +258,21 @@ subroutine psb_srgmres_vect(a,prec,b,x,eps,desc_a,info,&
     bni = psb_geamax(b,desc_a,info)
   else if (istop_ == 2) then 
     bn2 = psb_genrm2(b,desc_a,info)
+  else if (istop_ == 3) then
+    call psb_geaxpby(sone,b,szero,v(1),desc_a,info)
+    if (info /= psb_success_) then 
+      info=psb_err_from_subroutine_non_ 
+      call psb_errpush(info,name)
+      goto 9999
+    end if
+    
+    call psb_spmm(-sone,a,x,sone,v(1),desc_a,info,work=aux)
+    if (info /= psb_success_) then 
+      info=psb_err_from_subroutine_non_ 
+      call psb_errpush(info,name)
+      goto 9999
+    end if
+    r0n2 = psb_genrm2(v(1),desc_a,info)
   endif
   errnum = szero
   errden = sone
@@ -274,7 +289,6 @@ subroutine psb_srgmres_vect(a,prec,b,x,eps,desc_a,info,&
   
     ! compute r0 = b-ax0
     ! check convergence
-    ! compute v1 = r0/||r0||_2
 
     if (debug_level >= psb_debug_ext_) &
          & write(debug_unit,*) me,' ',trim(name),&
@@ -319,6 +333,10 @@ subroutine psb_srgmres_vect(a,prec,b,x,eps,desc_a,info,&
       rni = psb_genrm2(v(1),desc_a,info)
       errnum = rni
       errden = bn2
+    else if (istop_ == 3) then 
+      rni = psb_genrm2(v(1),desc_a,info)
+      errnum = rni
+      errden = r0n2
     endif
     if (info /= psb_success_) then 
       info=psb_err_from_subroutine_non_ 
@@ -397,6 +415,14 @@ subroutine psb_srgmres_vect(a,prec,b,x,eps,desc_a,info,&
         rni = abs(rs(i+1))
         errnum = rni
         errden = bn2
+      else if (istop_ == 3) then 
+        !
+        ! compute the residual 2-norm as byproduct of the solution
+        ! procedure of the least-squares problem
+        !
+        rni = abs(rs(i+1))
+        errnum = rni
+        errden = r0n2
       endif
 
       if (errnum <= eps*errden) then 
diff --git a/krylov/psb_z_krylov_conv_mod.f90 b/krylov/psb_z_krylov_conv_mod.f90
index f6e49dd5..46915450 100644
--- a/krylov/psb_z_krylov_conv_mod.f90
+++ b/krylov/psb_z_krylov_conv_mod.f90
@@ -48,13 +48,14 @@ Module psb_z_krylov_conv_mod
 
 contains
 
-  subroutine psb_z_init_conv(methdname,stopc,trace,itmax,a,b,eps,desc_a,stopdat,info)
+  subroutine psb_z_init_conv(methdname,stopc,trace,itmax,a,x,b,eps,&
+       & desc_a,stopdat,info)
     use psb_base_mod
     implicit none 
     character(len=*), intent(in)      :: methdname
     integer(psb_ipk_), intent(in)               :: stopc, trace, itmax
     type(psb_zspmat_type), intent(in) :: a
-    complex(psb_dpk_), intent(in)     :: b(:)
+    complex(psb_dpk_), intent(inout)     :: b(:), x(:)
     real(psb_dpk_), intent(in)        :: eps
     type(psb_desc_type), intent(in)   :: desc_a
     type(psb_itconv_type)             :: stopdat
@@ -62,6 +63,7 @@ contains
 
     integer(psb_ipk_) :: ictxt, me, np, err_act, ierr(5)
     character(len=20)                 :: name
+    complex(psb_dpk_), allocatable     :: r(:)
 
     info = psb_success_
     name = 'psb_init_conv'
@@ -88,6 +90,12 @@ contains
     case (2) 
       stopdat%values(psb_ik_bn2_) = psb_genrm2(b,desc_a,info)
 
+    case (3)
+      call psb_geall(r,desc_a,info)
+      call psb_geaxpby(zone,b,zzero,r,desc_a,info)
+      call psb_spmm(-zone,a,x,zone,r,desc_a,info)
+      stopdat%values(psb_ik_r0n2_) = psb_genrm2(r,desc_a,info)
+      call psb_gefree(r,desc_a,info)
     case default
       info=psb_err_invalid_istop_
       ierr(1) = stopc
@@ -152,6 +160,11 @@ contains
       stopdat%values(psb_ik_errnum_) = stopdat%values(psb_ik_rn2_)
       stopdat%values(psb_ik_errden_) = stopdat%values(psb_ik_bn2_)
 
+    case(3)
+      stopdat%values(psb_ik_rn2_)  = psb_genrm2(r,desc_a,info)
+      stopdat%values(psb_ik_errnum_) = stopdat%values(psb_ik_rn2_)
+      stopdat%values(psb_ik_errden_) = stopdat%values(psb_ik_r0n2_)
+
     case default
       info=psb_err_internal_error_
       call psb_errpush(info,name,a_err="Control data in stopdat messed up!")
@@ -188,20 +201,21 @@ contains
   end function psb_z_check_conv
 
 
-  subroutine psb_z_init_conv_vect(methdname,stopc,trace,itmax,a,b,eps,desc_a,stopdat,info)
+  subroutine psb_z_init_conv_vect(methdname,stopc,trace,itmax,a,x,b,eps,desc_a,stopdat,info)
     use psb_base_mod
     implicit none 
     character(len=*), intent(in)      :: methdname
     integer(psb_ipk_), intent(in)               :: stopc, trace,itmax
     type(psb_zspmat_type), intent(in) :: a
     real(psb_dpk_), intent(in)        :: eps
-    type(psb_z_vect_type), intent(inout)  :: b
+    type(psb_z_vect_type), intent(inout)  :: x, b
     type(psb_desc_type), intent(in)   :: desc_a
     type(psb_itconv_type)             :: stopdat
     integer(psb_ipk_), intent(out)              :: info
 
     integer(psb_ipk_) :: ictxt, me, np, err_act, ierr(5)
     character(len=20)                 :: name
+    type(psb_z_vect_type) :: r
 
     info = psb_success_
     name = 'psb_init_conv'
@@ -228,6 +242,12 @@ contains
     case (2) 
       stopdat%values(psb_ik_bn2_) = psb_genrm2(b,desc_a,info)
 
+    case (3)
+      call psb_geasb(r,desc_a,info,scratch=.true.)
+      call psb_geaxpby(zone,b,zzero,r,desc_a,info)
+      call psb_spmm(-zone,a,x,zone,r,desc_a,info)
+      stopdat%values(psb_ik_r0n2_) = psb_genrm2(r,desc_a,info)
+      call psb_gefree(r,desc_a,info)
     case default
       info=psb_err_invalid_istop_
       ierr(1) = stopc
@@ -293,6 +313,11 @@ contains
       stopdat%values(psb_ik_errnum_) = stopdat%values(psb_ik_rn2_)
       stopdat%values(psb_ik_errden_) = stopdat%values(psb_ik_bn2_)
 
+    case(3)
+      stopdat%values(psb_ik_rn2_)  = psb_genrm2(r,desc_a,info)
+      stopdat%values(psb_ik_errnum_) = stopdat%values(psb_ik_rn2_)
+      stopdat%values(psb_ik_errden_) = stopdat%values(psb_ik_r0n2_)
+
     case default
       info=psb_err_internal_error_
       call psb_errpush(info,name,a_err="Control data in stopdat messed up!")
diff --git a/krylov/psb_zbicg.f90 b/krylov/psb_zbicg.f90
index 57b81bb1..7d17a042 100644
--- a/krylov/psb_zbicg.f90
+++ b/krylov/psb_zbicg.f90
@@ -226,7 +226,7 @@ subroutine psb_zbicg_vect(a,prec,b,x,eps,desc_a,info,&
   itx   = 0
 
 
-  call psb_init_conv(methdname,istop_,itrace_,itmax_,a,b,eps,desc_a,stopdat,info)
+  call psb_init_conv(methdname,istop_,itrace_,itmax_,a,x,b,eps,desc_a,stopdat,info)
   if (info /= psb_success_) Then 
      call psb_errpush(psb_err_from_subroutine_non_,name)
      goto 9999
diff --git a/krylov/psb_zcg.F90 b/krylov/psb_zcg.F90
index 23e25141..87f4d43a 100644
--- a/krylov/psb_zcg.F90
+++ b/krylov/psb_zcg.F90
@@ -222,7 +222,7 @@ subroutine psb_zcg_vect(a,prec,b,x,eps,desc_a,info,&
 
     rho = zzero
     
-    call psb_init_conv(methdname,istop_,itrace_,itmax_,a,b,eps,desc_a,stopdat,info)
+    call psb_init_conv(methdname,istop_,itrace_,itmax_,a,x,b,eps,desc_a,stopdat,info)
     if (info /= psb_success_) Then 
       call psb_errpush(psb_err_from_subroutine_non_,name)
       goto 9999
diff --git a/krylov/psb_zcgs.f90 b/krylov/psb_zcgs.f90
index ba68ddb3..fe179ef2 100644
--- a/krylov/psb_zcgs.f90
+++ b/krylov/psb_zcgs.f90
@@ -200,7 +200,7 @@ Subroutine psb_zcgs_vect(a,prec,b,x,eps,desc_a,info,&
 
   itx   = 0
 
-  call psb_init_conv(methdname,istop_,itrace_,itmax_,a,b,eps,desc_a,stopdat,info)
+  call psb_init_conv(methdname,istop_,itrace_,itmax_,a,x,b,eps,desc_a,stopdat,info)
   if (info /= psb_success_) Then 
      call psb_errpush(psb_err_from_subroutine_non_,name)
      goto 9999
diff --git a/krylov/psb_zcgstab.f90 b/krylov/psb_zcgstab.f90
index 599b8429..cedc6cd5 100644
--- a/krylov/psb_zcgstab.f90
+++ b/krylov/psb_zcgstab.f90
@@ -215,7 +215,7 @@ Subroutine psb_zcgstab_vect(a,prec,b,x,eps,desc_a,info,itmax,iter,err,itrace,ist
   End If
 
   itx   = 0
-  call psb_init_conv(methdname,istop_,itrace_,itmax_,a,b,eps,desc_a,stopdat,info)
+  call psb_init_conv(methdname,istop_,itrace_,itmax_,a,x,b,eps,desc_a,stopdat,info)
   if (psb_errstatus_fatal()) Then 
     call psb_errpush(psb_err_from_subroutine_non_,name)
     goto 9999
diff --git a/krylov/psb_zcgstabl.f90 b/krylov/psb_zcgstabl.f90
index eca398e7..bd78e9f9 100644
--- a/krylov/psb_zcgstabl.f90
+++ b/krylov/psb_zcgstabl.f90
@@ -245,7 +245,7 @@ Subroutine psb_zcgstabl_vect(a,prec,b,x,eps,desc_a,info,&
   rt0 => wwrk(10)
   
 
-  call psb_init_conv(methdname,istop_,itrace_,itmax_,a,b,eps,desc_a,stopdat,info)
+  call psb_init_conv(methdname,istop_,itrace_,itmax_,a,x,b,eps,desc_a,stopdat,info)
   if (info /= psb_success_) Then 
      call psb_errpush(psb_err_from_subroutine_non_,name)
      goto 9999
diff --git a/krylov/psb_zfcg.F90 b/krylov/psb_zfcg.F90
index 8a30c591..4380ee20 100644
--- a/krylov/psb_zfcg.F90
+++ b/krylov/psb_zfcg.F90
@@ -209,7 +209,7 @@ subroutine psb_zfcg_vect(a,prec,b,x,eps,desc_a,info,&
        & scratch=.true.,mold=x%v)
 
 
-    call psb_init_conv(methdname,istop_,itrace_,itmax_,a,b,eps,desc_a,stopdat,info)
+    call psb_init_conv(methdname,istop_,itrace_,itmax_,a,x,b,eps,desc_a,stopdat,info)
   itx=0
 
   restart: do 
diff --git a/krylov/psb_zgcr.f90 b/krylov/psb_zgcr.f90
index a19a7b4f..4dbfe3f8 100644
--- a/krylov/psb_zgcr.f90
+++ b/krylov/psb_zgcr.f90
@@ -246,7 +246,7 @@ subroutine psb_zgcr_vect(a,prec,b,x,eps,desc_a,info,&
   itx = 0
   
   nrst = -1
-  call psb_init_conv(methdname,istop_,itrace_,itmax_,a,b,eps,desc_a,stopdat,info)
+  call psb_init_conv(methdname,istop_,itrace_,itmax_,a,x,b,eps,desc_a,stopdat,info)
   restart: do 
     if (itx>= itmax_) exit restart 
     h = zzero
diff --git a/krylov/psb_zrgmres.f90 b/krylov/psb_zrgmres.f90
index 68d25f85..26209935 100644
--- a/krylov/psb_zrgmres.f90
+++ b/krylov/psb_zrgmres.f90
@@ -137,7 +137,7 @@ subroutine psb_zrgmres_vect(a,prec,b,x,eps,desc_a,info,&
   integer(psb_ipk_) :: itx, i, istop_, err_act
   integer(psb_ipk_) :: debug_level, debug_unit
   integer(psb_ipk_) :: ictxt, np, me  
-  Real(psb_dpk_)     :: rni, xni, bni, ani,bn2, dt
+  Real(psb_dpk_)     :: rni, xni, bni, ani,bn2, dt, r0n2
   real(psb_dpk_)     :: errnum, errden, deps, derr
   character(len=20)           :: name
   character(len=*), parameter :: methdname='RGMRES'
@@ -258,6 +258,21 @@ subroutine psb_zrgmres_vect(a,prec,b,x,eps,desc_a,info,&
     bni = psb_geamax(b,desc_a,info)
   else if (istop_ == 2) then 
     bn2 = psb_genrm2(b,desc_a,info)
+  else if (istop_ == 3) then
+    call psb_geaxpby(zone,b,zzero,v(1),desc_a,info)
+    if (info /= psb_success_) then 
+      info=psb_err_from_subroutine_non_ 
+      call psb_errpush(info,name)
+      goto 9999
+    end if
+    
+    call psb_spmm(-zone,a,x,zone,v(1),desc_a,info,work=aux)
+    if (info /= psb_success_) then 
+      info=psb_err_from_subroutine_non_ 
+      call psb_errpush(info,name)
+      goto 9999
+    end if
+    r0n2 = psb_genrm2(v(1),desc_a,info)
   endif
   errnum = zzero
   errden = zone
@@ -274,7 +289,6 @@ subroutine psb_zrgmres_vect(a,prec,b,x,eps,desc_a,info,&
   
     ! compute r0 = b-ax0
     ! check convergence
-    ! compute v1 = r0/||r0||_2
 
     if (debug_level >= psb_debug_ext_) &
          & write(debug_unit,*) me,' ',trim(name),&
@@ -319,6 +333,10 @@ subroutine psb_zrgmres_vect(a,prec,b,x,eps,desc_a,info,&
       rni = psb_genrm2(v(1),desc_a,info)
       errnum = rni
       errden = bn2
+    else if (istop_ == 3) then 
+      rni = psb_genrm2(v(1),desc_a,info)
+      errnum = rni
+      errden = r0n2
     endif
     if (info /= psb_success_) then 
       info=psb_err_from_subroutine_non_ 
@@ -397,6 +415,14 @@ subroutine psb_zrgmres_vect(a,prec,b,x,eps,desc_a,info,&
         rni = abs(rs(i+1))
         errnum = rni
         errden = bn2
+      else if (istop_ == 3) then 
+        !
+        ! compute the residual 2-norm as byproduct of the solution
+        ! procedure of the least-squares problem
+        !
+        rni = abs(rs(i+1))
+        errnum = rni
+        errden = r0n2
       endif
 
       if (errnum <= eps*errden) then