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m Signing comment by 213.22.50.11 - "→Convergence: Bisection method not a linear method" |
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I don’t agree with the statement that the bisection method has a linear convergence or, in other words, a 1st order convergence. The classification of a 1st order method has to do with the error along the sequence (distance between the successive values and the root) and not with the estimation of the absolute maximal error, incidentally quite imprecise in the bisection method.
In the 1st order methods the observation of the sequence of values converging to the root reveals a steady increase in the number of correct figures. On the contrary, through the bisection method it is possible for the distance to the root to increase in two consecutive iterations. It follows that the bisection method is just a method that narrows the interval that contains the root, halving it on each iteration. It doesn’t guarantee the same happens with the distance to the root, therefore it is not a 1st order method. Ana Maria Faustino 20 March 2013 (FEUP) <span style="font-size: smaller;" class="autosigned">— Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/213.22.50.11|213.22.50.11]] ([[User talk:213.22.50.11|talk]]) 02:46, 20 March 2013 (UTC)</span><!-- Template:Unsigned IP --> <!--Autosigned by SineBot-->
== Computation of the midpoint ==
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