A generalized multivariable Newton method

Abstract It is well known that the Newton method may not converge when initial guess does belong to a specific quadratic convergence region. We propose family of new variants with potential advantage having larger region as more desirable properties near solution. prove family, and provide bounds for asymptotic error constant. illustrate advantages methods by means test problems, including two six variable polynomial systems, challenging signal processing example. present numerical experimental methodology which uses large number randomized guesses from in turn providing advice employed preferable use particular search domain.