High order iterative schemes for quadratic equations (Q937190)

A bi-parametric family of higher-order iterative methods including some well known iterative processes (among them the classical Chebyshev method) is studied for solving quadratic equations. The main advantage of the methods under consideration is that all the corresponding linear systems are associated with the same matrix. A semilocal convergence theorem is proved and some applications to partial differential equations, in particular, for the Poisson equaton is discussed. Finally, some results of numerical experiments confirming the proposed theoretical considerations are presented.