A TOTAL ALGORITHM FOR POLYNOMIAL ROOTS BASED UPON BAIRSTOW'S METHOD

Ault, David A. (1974) A TOTAL ALGORITHM FOR POLYNOMIAL ROOTS BASED UPON BAIRSTOW'S METHOD . Technical Report CS74002-R, Computer Science, Virginia Tech.

Abstract

This program uses Bairstow's method to find the real and complex roots of a polynomial with real coefficients. There are several reasons for developing a routine based upon Bairstow's method. It is sometimes the case that all of the roots of a polynomial with real coefficients are desired. Bairstow's method provitles an iterative process for finding both the real and complex roots using only real arithmetic. Further, since it is based on Newton's method for a system of two nonlinear equations in two unknowns, it has the rapid convergence property of Newton's method for systems of equations. The major drawback of this method is that it sometimes fails to converge [11, p. 110]. This is because it is difficult to find an initial starting guess which satisfies the strict conditions necessary to assure convergence. When these conditions are not satisfied, the sequence of approximations may jump away from the desired roots or may iterate away from the roots indefinitely.