Extraction of Innnite Zeros of Polynomial Matrices

نویسندگان

  • Didier Henrion
  • Javier Ruiz
  • Michael Sebek
چکیده

An algorithm is described for computing the structure at innnity and extracting the innnite zeros of a given polynomial matrix. The algorithm relies on numerically reliable operations only. Applications include computation of the subspace of impulsive solution of a set of linear diierential equations, derivation of the Smith form at innnity of a polynomial matrix, or also enhanced computation of the poles of a linear system described by polynomial matrix fractions. The numerical routines described in this paper are implemented in the new release 3.0 of the Polynomial Toolbox for Matlab.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Inequalities for the polar derivative of a polynomial with $S$-fold zeros at the origin

‎Let $p(z)$ be a polynomial of degree $n$ and for a complex number $alpha$‎, ‎let $D_{alpha}p(z)=np(z)+(alpha-z)p'(z)$ denote the polar derivative of the polynomial p(z) with respect to $alpha$‎. ‎Dewan et al proved‎ ‎that if $p(z)$ has all its zeros in $|z| leq k, (kleq‎ ‎1),$ with $s$-fold zeros at the origin then for every‎ ‎$alphainmathbb{C}$ with $|alpha|geq k$‎, ‎begin{align*}‎ ‎max_{|z|=...

متن کامل

On the $s^{th}$ derivative of a polynomial

For every $1leq s< n$, the $s^{th}$ derivative of a polynomial $P(z)$ of degree $n$ is a polynomial $P^{(s)}(z)$ whose degree is $(n-s)$. This paper presents a result which gives generalizations of some inequalities regarding the $s^{th}$ derivative of a polynomial having zeros outside a circle. Besides, our result gives interesting refinements of some well-known results.

متن کامل

On the polar derivative of a polynomial

For a polynomial p(z) of degree n, having all zeros in |z|< k, k< 1, Dewan et al [K. K. Dewan, N. Singh and A. Mir, Extension of some polynomial inequalities to the polar derivative, J. Math. Anal. Appl. 352 (2009) 807-815] obtained inequality between the polar derivative of p(z) and maximum modulus of p(z). In this paper we improve and extend the above inequality. Our result generalizes certai...

متن کامل

Extending the Notions of Companion and Innnite Companion to Matrix Polynomials Extending the Notions of Companion and Innnite Companion to Matrix Polynomials

An extended innnite companion matrix ~ C 1 (D) and an innnite companion matrix C 1 (D) for a (nonmonic in general) matrix polynomial D is introduced and the nite companion matrix C(D) is generalized to the nonmonic case. These matrices generalize all properties of the innnite and nite companion (Frobenius) matrix corresponding to a scalar polynomial. In particular, C 1 (D) is a controllability ...

متن کامل

A Toeplitz algorithm for polynomial J-spectral factorization

A block Toeplitz algorithm is proposed to perform the J-spectral factorization of a para-Hermitian polynomial matrix. The input matrix can be singular or indefinite, and it can have zeros along the imaginary axis. The key assumption is that the finite zeros of the input polynomial matrix are given as input data. The algorithm is based on numerically reliable operations only, namely computation ...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2000