On the local convergence of a quasi-Newton method for solving matrix polynomial equations

Abstract

In this article, we propose a quasi-Newton algorithm to solve a matrix polynomial equation, which can be seen as a generalization of the algorithm of the same type to solve the matrix quadratic equation proposed in Macías et al. (2016). The proposed algorithm reduces the computational cost of the Newton–Schur method traditionally used to solve this type of equations. We show that this algorithm is local and even quadratically convergent. Finally, we present numerical experiments that ratify the theoretical results developed.