An improved diagonal Jacobian approximation via a new quasi-Cauchy condition for solving large-scale systems of nonlinear equations

We present a new diagonal quasi-newton update with an improved diagonal jacobian approximation for solving large-scale systems of nonlinear equations. in this approach,the jacobian approximation is derived based on the quasi-cauchy condition. the anticipation has been to further improve the performance of diagonal updating,by modifying the quasi-cauchy relation so as to carry some additional information from the functions. the effectiveness of our proposed scheme is appraised through numerical comparison with some well-known newton-like methods. © 2013 mohammed yusuf waziri and zanariah abdul majid.