Scale invariant quasi-Newton methods for the solution of nonlinear equations

Abstract Sufficient conditions for a rank-one quasi-Newton method for solving systems of algebraic nonlinear equations being scale invariant are derived. Methods which are invariant under changes in the scale of the equations with a general matrix and with diagonal matrices for the variables are proposed The convergence results of [2] are extended in order to show local superlinear convergence of the new scale invariant methods. Extensive numerical tests of the proposed methods are performed showing the superiority of the new methods especially on “badly scaled” problems.