Two global quasi-Newton algorithms for solving matrix polynomial equations

In this article, we globalize the quasi-Newton algorithm proposed in Macias et al. (Appl Math Comput 441:127678, 2023) introducing an exact line search, we propose a polynomial approximation to the merit function and we deduce a sufficient condition for its minimization interval. We use the exact merit function and its approximation to propose two global quasi-Newton algorithms for solving matrix polynomial equations. For each algorithm, we prove that the exact line search does not affect the convergence of quasi-Newton method. In addition, we present comparative numerical tests of the algorithmic proposals in which we also compare with global Newton's method.