\chapter{Concluding Remarks}\label{ch: conclusion}

An implementation of the thin-QR factorization and limited memory BFGS has been presented, in particular with exact line search in order to solve more efficiently the least squares problem. Convergence for both methods have been proven and tested.
An implementation of BFGS and DFP, with both exact line search and trust region method using the dogleg method, and SR1 have been implemented and tested.
From the experiments it is pretty clear that L-BFGS is better than all other Quasi-Newton methods for solving the least squares problem, even when using a small parameter for the memory. Instead the QR method performs better when solving for ill-conditioned matrices, but the memory usage is higher.