= (+) &\a=(+) is=(-) d l , = ( + ) &,=(+I related to Fe(s)+(dFe(s)/ds) and thus the root distribution is ascertained. However, in this case F&) can be simply factored as Fe(s)=(s2+2)(s2+ 1).This indicates that four roots are on the ima-gin-q-;u(i_s. From the inners determinants sign shown in Fig. 5, Var[l,A,,A4,A6,As,Alo,AlJ=2 and we have two roots in right half of s plane and therefore four roots exist in the left half of s plane. This agrees with the authors results.In conclusion, it may be remarked that the double triangulwtion procedure for all critical cases can also be used for determining the root distribution of a real polynomial within the unit circle or other regions in the complex plane [3]. This offers a unified approach for all these cases. As a final note, one may mention that the multiplication (s+c) by the polynomial is performed directly to the offending polynomial and need not be done to the original polynomial as remarked in some publications [I], [6]. Furthermore, Gantmachefs procedure [4], though correct, is very complicated. It involves the use of Routh table, Euclid algorithm, and Sturm test to tackle these critical cases.
ACKNOWLEDGENTThe author acknowledges the aid of N. A. Pendergass in the computer study of this note. pp. 280-286: E I. Jury and S. M. Ahn, "A computational algorithm for innem" IEEE T m .If the authors of the above correspondence' had made all the possible approximations due to the fact of e being an arbitrarily s m a l l number, they would have found that the total number of sign changes was independent of the sign of c, and more, they would have clearly noted the existence of all-zero rows in both Examples 2 and 3, indicating that the polynomials under test either had roots on the jo-axis or roots symmetrically spaced with reference to the j o -a x i s in the left-hand and the right-hand planes. In fact, for
D(s)=s6+s5+3s4+3s3+3s2+2s+1Manuscript
