% LaTeX template for submitting an abstract to  
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%           SWIM 2026
%           22-24 June 2026
%           Kraków, Poland
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\documentclass[14pt, a4paper]{article}

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\usepackage{extsizes}
\usepackage{amsmath}
\usepackage{amsthm}
\usepackage{amssymb}
\usepackage{url}
\usepackage{graphicx}
% please use UTF8 for the encoding!!!
\usepackage[utf8]{inputenc}

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%\renewcommand{\cite}[1]{{[\ref{#1}]}}
%\renewcommand{\bibitem}[1]{\refstepcounter{enumi}\item[{[\arabic{enumi}]}]\label{#1}}
%\renewenvironment{bibliography}[1][1]{\subsection*{References}\setcounter{enumi}{0}\begin{enumerate}}{\end{enumerate}}

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% DEFINITIONS
\newtheorem{prop}{Proposition}

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%\usepackage{solvehaltingproblem}

% AUTHORS - if all affiliations are the same, upper indices can be excluded
\newcommand\authors{Author One$^{1}$, Author Two $^{1}$ and Author Three$^{2}$}

% TITLE - required 
\newcommand\papertitle{On Solving a Problem using Interval Methods}

\begin{document}

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% AFFILIATION - required with address, email at least for corresponding author
{\small
$^{1}$ Affiliation 1\\
Address 1\\
\texttt{\{author.one,author.two\}@domain1}\\
$^{2}$ Affiliation 2\\
Address 2\\
\texttt{author.three@domain2}
}

\end{center}

\bigskip

% KEYWORDS - required
{\noindent\bf Keywords:} Mathematics, Computer Science, Interval Methods

% MAIN PART - Please use subsection first and without numbering.
\subsection*{Introduction}
Interval methods~\cite{moore:kearfott:cloud:2009} are an approach to numerical computation which provide guaranteed bounds on the range of a quantity or function~\cite{moore:1976}.

\subsection*{Basic properties}
The main property of interval methods is the inclusion property: If the arguments of an interval extension of an operator contain the true values, then so does the result.
\begin{prop}
If $x\in[x]$ and $y\in[y]$, then $x+y \in [x] \; [+] \; [y]$.
\end{prop}


\subsection*{Main results}
If $[f]$ is an interval extension of $f$, then
\begin{equation*}
x\in [x] \implies f(x) \in [f]([x]) .
\end{equation*}

\subsubsection*{Acknowledgement}
Thanks to the National Institute of Interval Methods.

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\begin{thebibliography}{1}
\bibitem{moore:1976}
R.~Moore.
\newblock On computing the range of a rational function of $n$ variables over a
  bounded region.
\newblock {\em Computing}, 16:1--15, 1976.

\bibitem{moore:kearfott:cloud:2009}
R.E. Moore, R.B. Kearfott, and M.J. Cloud.
\newblock {\em Introduction to Interval Analysis}.
\newblock Society for Industrial and Applied Mathematics, 2009.
\end{thebibliography}

\end{document}