علیرضا عطایی

The least squares problems in numerical analysis is one of the most important issues. In this thesis, we proposed to preconditioned the GMRES method by using incomplete Givens orthogonalization (IGO) method for the solution of large sparse linear least squares problems. Theoretical analysis shows that the preconditioner the satisfies the sufficient condition that can guarantee that the preconditioned GMRES method will never break down and always give the least- squares solution of the original problem.