An autoadaptative limited memory Broyden’s method to solve systems of nonlinear equations

We propose a new Broyden-like method that we call autoadaptative limited memory method. Unlike classical limited memory method, we do not need to set any parameters such as the maximal size, that solver can use. In fact, the autoadaptative algorithm automatically increases the approximate subspace when the convergence rate decreases. The convergence of this algorithm is superlinear under classical hypothesis. A few numerical results with well-known benchmarks functions are also provided and show the efficiency of the method.