Newton-like method for nonlinear banded block diagonal system

We present an efficient Newton-like method for solving systems of nonlinear equations with banded block diagonal structure. Such systems arise in economic models. The main idea of this method is to exploit the special structure of the Jacobian in a Newton-like method. The proposed algorithm uses an iterative method for calculation of the approximation of diagonal blocks in the Jacobian. Depending on dimensions of blocks significant reduction in computational cost is obtained and the algorithm can be easily parallelized. Local convergence of the proposed method is proved and some numerical results are presented.