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195 %% \end{frame} |
195 %% \end{frame} |
196 |
196 |
197 \begin{frame}[fragile] |
197 \begin{frame}[fragile] |
198 \frametitle{Bisection Method} |
198 \frametitle{Bisection Method} |
199 \begin{enumerate} |
199 \begin{enumerate} |
200 \item Start with an interval $(a, b)$ within wphich a root exists |
200 \item Start with an interval $(a, b)$ within which a root exists |
201 \item $f(a)\cdot f(b) < 0$ |
201 \item $f(a)\cdot f(b) < 0$ |
202 \item Bisect the interval. $c = \frac{a+b}{2}$ |
202 \item Bisect the interval. $c = \frac{a+b}{2}$ |
203 \item Change the interval to $(a, c)$ if $f(a)\cdot f(c) < 0$ |
203 \item Change the interval to $(a, c)$ if $f(a)\cdot f(c) < 0$ |
204 \item Else, change the interval to $(c, b)$ |
204 \item Else, change the interval to $(c, b)$ |
205 \item Go back to 3 until $(b-a) \le$ tolerance |
205 \item Go back to 3 until $(b-a) \le$ tolerance |