Solving Polynomial Equations using Modified Super Ostrowski Homotopy Continuation Method

Abstract

Homotopy continuation methods (HCMs) are now widely used to find the roots of polynomial equations as well as transcendental equations.  HCM can be used to solve the divergence problem as well as starting value problem. Obviously, the divergence problem of traditional methods occurs when a method cannot be operated at the beginning of iteration for some points, known as bad initial guesses. Meanwhile, the starting value problem occurs when the initial guess is far away from the exact solutions.   The starting value problem has been solved using Super Ostrowski homotopy continuation method for the initial guesses between . Nevertheless, Super Ostrowski homotopy continuation method was only used to find out real roots of nonlinear equations.  In this paper, we employ the Modified Super Ostrowski-HCM to solve several real life applications which involves polynomial equations by expanding the range of starting values. The results indicate that the Modified Super Ostrowski-HCM performs better than the standard Super Ostrowski-HCM. In other words, the complex roots of polynomial equations can be found even the starting value is real with this proposed scheme.