Following Davidon′s criterion of optimal iterative correction,a three-step quasi Newton method of nocorrection matrix stored is constructed for unconst rained optimization problems and applied to the solution of a large-scale complicated system of linearill-conditioned equations.Numerical studies show that the method is simple in calculation,quick for convergence and robustinill-condition resistance so good as to compare to a recursional gorithm and even for well-conditioned equations it is fast in computation,and small in storage size.It is thereby possible to further improve the application of non-conventional data in objective analysis and quality of medium-and small-scale wether system analysis.