A CONTROL-BASED APPROACH TO THE SOLUTION OF NONLINEAR ALGEBRAIC EQUATIONS

A different approach to the solution of a nonlinear set of algebraic e quations is presented. It is basically a revision of the Newton iterat ive algorithm from a digital control point of view, The Newton algorit hm is considered like a digital control algorithm that acts on a set o f nonlinear algebraic equations. Its target is to find a value x that satisfies the algebraic equation set. This value can be considered as a particular ''input'' of the equation set which gives a zero ''outpu t'' while the iteration index can be considered as the clock of the di gital system. From this point of view some correlations between the st ability of digital systems and the Newton algorithm can be shown, This approach allows us to understand the reasons behind the convergence f ailure of some modified Newton algorithms such as source stepping, dam ping, and limiting that literature often reports as heuristic.