Linear recurrent sequences and polynomial roots (Q1394940)

The authors obtain bounds on the roots (possibly several) of the largest absolute value of a complex polynomial by using recurrent sequences for which it is the characteristic polynomial. They conclude with a discussion of the effectiveness of a rule given in 1884 by Jacobi, in which he introduces the polynomial whose roots are the dominant roots of the given polynomial. Specific examples are given. [While Proposition 7 appears to be correct, a modification of the proof seems required to make it work].