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    Mathematical background

    Let a system of $n$ equations in $n$ unknowns $ F=\{ F_i(x_1,\ldots,x_n)=0, i\in [1,n]\} $ each $F_i$ being at least $C^1$. Let ${\bf X}$ be a range vector for $\{x_1,\ldots,x_n\}$, $y$ a point inside ${\bf X}$ and $Y$ an arbitrary nonsingular real matrix. Let define $K$ as:

    \begin{displaymath} K{\bf X}=y-YF(y)+\{I-YF^\prime({\bf X})\}({\bf X}-y) \end{displaymath}

    and let $r_0$ be the norm of the matrix $I-YF^\prime({\bf X})$. If

    \begin{displaymath} K({\bf X}) \subseteq {\bf X}~~~{\rm and}~~r_0<1 \end{displaymath}

    then there is a unique solution [16] of $F$ in ${\bf X}$. This unique solution can be found using Krawczyk solving method (see section 2.10).

    next up previous contents index Next: Implementation Up: Moore theorem Previous: Moore theorem
  • La page de J-P. Merlet
  • J-P. Merlet home page
  • La page Présentation de COPRIN
  • COPRIN home page
  • La page "Présentation" de l'INRIA
  • INRIA home page

    Jean-Pierre Merlet