paper1.tex

   1 \documentclass[11pt,a4paper]{article}
   2 \usepackage[latin1]{inputenc}
   3 \usepackage{amsmath}
   4 \usepackage{amsfonts}
   5 \usepackage{amssymb}
   6 \author{ghidouche}
   7 \title{Paper1_kahina}
   8 \begin{document}
   9 \section{Root finding problem}
  10 we consider a polynomial
  11 $p(x)=\sum{a_{i}x^{i}}=a_{n}\prod(x-\alpha_{i}), a_{0} a_{n}\neq0,$
  12 of degree \textit{n}having coefficients in the complex \textit{c} and zeros \alpha_{i},\textit{i=1,...,n}.
  13 the root finding problem consiste to find all n root of \textit{p(x)}. the problem of finding a root is equivalent to the problem of finding a fixed-point. To see this consider the fixed-point problem of finding the
  14 n-dimensional vector x such that
  15
  16 \end{document}