On the use of Davidenko´s method in complex root search

Davidenko´s method has proved to be a powerful technique for solving a system of n-coupled nonlinear algebraic equations. It uses a Newton´s method reduction to produce n-coupled first-order differential equations in a dummy variable. The advantage it offers over Newton´s method and other traditional methods such as Muller´s method is that it relaxes the restrictions that the initial guess has to be very close to the solution. Two examples involving the search for complex roots are presented. Davidenko´s method seems to converge to the roots for all the arbitrary initial guesses considered while Muller´s method appears to fail for some cases. This suggests the use of Davidenko´s method as an alternative to Muller´s method when the later fails to converge or is slowly convergent