Let K be a bounded linear operator from Hilbert space $H_1$ into Hilbert space $H_2$. When numerically solving the first kind equation Kf = g, one usually picks n orthonormal functions $phi_1, phi_2,...,phi_n$ in $H_1$ which depend on the numerical method and on the problem, see Varah [12] for more details. Then one findes the unique minimum norm element $f_M in M$ that satisfies $Vert K f_M - g Vert = inf {Vert K f - g Vert : f in M}$, where M is the linear span of $phi_1, phi_2,...,phi_n$. Such a solution $f_M in M$ is called the M-solution of K f = g. Some methods for finding the M-solution of K f = g were proposed by Banks [2] and Marti [9,10]. See [5,6,8] for convergence results comparing the M-solution of K f = g with $f_0$, the least squares solution of minimum norm (LSSMN) of K f = g.