The polar decomposition of block companion matrices
Computers & Mathematics with Applications
Finding the maximum module of the roots of a polynomial by particle swarm optimization
ICSI'10 Proceedings of the First international conference on Advances in Swarm Intelligence - Volume Part I
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Let $C(p)$ denote the companion matrix of a monic polynomial $p$ with complex coefficients. Then the zeros of $p$ are exactly the eigenvalues of $C(p)$. In this paper, the singular values of $C(p)$ are computed. Applying some basic eigenvalue-singular value majorization relations, several sharp estimates are obtained for the zeros of $p$ in terms of its coefficients. These estimates improve some classical bounds on zeros of polynomials.