A numerical accuracy consideration in polynomial deflation

Abstract

In a recent paper, Peters and Wilkinson described a composite deflation method which provides an accurate technique for the determination of the roots of a polynomial where these roots are widely spaced. By examples involving deflation by linear factors they demonstrated that the method was much more accurate than forward or backward deflation. In addition, they stated that the method could also be used when deflating by a quadratic factor or a polynomial of higher degree. In this short note it is shown that composite deflation by quadratic factors can lead to severe rounding error where two successive deflations by linear factors produce a perfectly accurate result.