1)--in particular the

characteristic polynomial [gamma]N of A itself--in less than 6N additions (subtractions) and less than 4N multiplications (divisions), it is entirely feasible to find the roots of this polynomial (the eigenvalues of A) by Sturm plus bisection.

Thus, the closed loop

characteristic polynomial is (for simplicity, the operator [q.

When P is ranked, the generating function for [mu] is called the

characteristic polynomial and is given by

S]([lambda]) is the

characteristic polynomial of the shape operator of M, then we have

2] (say) and the

characteristic polynomial can be written as

i](f) are reflection vectors of the

characteristic polynomial f(z) of the nominal closed-loop system (3).

This method is based on approximation of secular function by using the Taylor series

characteristic polynomial of R SPDTM The

characteristic polynomial has been approximated with the polynomial of the third order from the Taylor series because it is easy to calculate [p".

The remainder of this paper is organized as follows: In Section 2, we briefly describe the Frobenius endomorphism on Jacobian groups of hyperelliptic curves over finite fields and a lemma contributed to Weil's theorem((5)), and in this section, we also introduce the Euclidean length in the algebraic integral ring Z[[tau]] with [tau] a root of some hyperelliptic curve's

characteristic polynomial.

We shall call the right side of formula [member of] the

characteristic polynomial of the node [V.

The objective of this section is to determine the ranges of PID controller gains for which this

characteristic polynomial is standard Hurwitz.

In this paper we propose new modification of Newton's method for the computation of the roots of the

characteristic polynomial of a real symmetric positive definite Toeplitz matrix.

Minimum code [6],

characteristic polynomial of matrix [7], identification code [8], link path code [9], summation polynomial [10], are used to characterize the kinematic chains.