Numerical Methods for Solving High Order Polynomial Equations

The problem of finding the roots of a polynomial equation is important because many calculations in engineering and scientific computation can be summarized to it. An adaptive algorithm based on Sturm's theorem which could find the isolate intervals for all the real roots rapidly is used to locate all the roots. To find the numerical root, they will first be roughly approximated by dichotomy method. And then these roots are computed by Newton method using the initial values got in the first step. This method overcomes the shortcomings of dichotomy method and iterative method. The first step could find a good initial point quickly for Newton method, and Newton method converges faster than dichotomy method. Numerical example shows the effectiveness of this method.