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Mathematical background

Let $P(x)$ be an univariate polynomial of degree $n$:

\begin{displaymath}
P(x)= a_n x^n + a_{n-1} x^{n-1}+.....a_0=0
\end{displaymath}

with $a_0a_n \not=0$. Let

\begin{displaymath}
A= max\{\mid a_{n-1}\mid ,\mid a_{n-2}\mid ,...,\mid a_0\mid...
...ime=max\{\mid a_n\mid ,\mid a_{n-1}\mid ,.....,\mid a_1\mid \}
\end{displaymath}

Then the modulus of any root $x_k$ of $P(x)=0$ verify:

\begin{displaymath}
\frac{1}{1+\frac{A^\prime}{\mid a_0\mid }}<\mid x_k\mid < 1 + \frac{A}{\mid a_n\mid }
\end{displaymath}



Jean-Pierre Merlet 2012-12-20