From: Kahina Date: Thu, 5 Nov 2015 09:23:52 +0000 (+0100) Subject: new X-Git-Url: https://bilbo.iut-bm.univ-fcomte.fr/and/gitweb/kahina_paper1.git/commitdiff_plain/1df92e2629fef95f9b236c8d952d94c08f5f34a0 new --- diff --git a/paper.tex b/paper.tex index f227762..1d70450 100644 --- a/paper.tex +++ b/paper.tex @@ -321,8 +321,8 @@ With high degree polynomial, the Ehrlich-Aberth method implementation, as well as the Durand-Kerner implement, suffers from overflow problems. This situation occurs, for instance, in the case where a polynomial having positive coefficients and a large degree is computed at a -point $\xi$ where $|\xi| > 1$, where $|x|$ stands for the modolus of a complex $x$. Indeed, the limited number in the -mantissa of floating points representations makes the computation of p(z) wrong when z +point $\xi$ where $|\xi| > 1$, where $|z|$ stands for the modolus of a complex $z$. Indeed, the limited number in the +mantissa of floating points representations makes the computation of $p(z)$ wrong when z is large. For example $(10^{50}) +1+ (- 10^{50})$ will give the wrong result of $0$ instead of $1$. Consequently, we can not compute the roots for large degrees. This problem was early discussed in