For an
n
n
th order linear boundary value problem
L
f
=
g
0
Lf = {g_0}
in the Hilbert space
L
2
[
a
,
b
]
{L^2}[a,b]
, a sequence of approximate solutions is constructed which converges to the unique least squares solution of minimal norm. The method is practical from a computational viewpoint, and it does not require knowing the null spaces of the differential operator
L
L
or its adjoint
L
∗
{L^ \ast }
.