The idea of using two-point stepsize gradient methods for solving unconstrained minimization problems on $\mathbb{R}^n$ is applied on computing the least-squares solutions of a given linear system. Special attention is paid on corresponding modification of the scalar correction method introduced in [1].
Additionally, we consider the gradient iterative schemes as a useful tool for computing the Drazin-inverse solution of an appropriate linear system. The functionality of the exposed algorithms is based on a specific representation of the Drazin inverse solution, as well as the properties that we have studied [3].

References:

[1]  M. Miladinović, P. Stanimirović, S. Miljković, Scalar Correction Method for Solving Large Scale Unconstrained Minimization Problems, J. Optim. Theory. Appl. 151 (2011), 304-320.

[2]  S. Miljković, M. Miladinović, P. Stanimirović, D. Đorđević, Scalar correction method for finding least-squares solutions on Hilbert spaces and its applications, Appl. Math. Comput. 219 (2013), 9639-9651.

[3]  S. Miljković, M. Miladinović, P. Stanimirović, Y. Wei, Gradient methods for computing the Drazin-inverse solution, J. Comput. Appl. Math. 253 (2013), 255-263.