Talk:Bisection method: Difference between revisions

Revision as of 02:47, 20 March 2013

Latest revision as of 15:51, 20 March 2024

(12 intermediate revisions by 5 users not shown)

Line 1:

{{WikiProject banner shell|class=Start|vital=yes|1=

{{maths rating|class=start|importance=mid|field=analysis}}

{{WikiProject Mathematics|importance=mid}}

}}

== Number of iterations for certain Tolerance ==

I think a little more should be added to this page about the number of iterations of the Bisection Method is needed to get the function within a certain Tolerance. By modeifying Theorem 2.1 from Numerical Analysis 8th edition, a quick bound approximation to the error can be found. Even know the actual error can be much smaller, it gives a good estimate of how long a function will take to converge by the Bisection Method. I would like to add info about this

Line 59 ⟶ 60:

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. User: 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 ==

Line 158 ⟶ 159:

: Could this be combined with the pseudocode already there?

: [[User:Mjmohio|Mjmohio]] ([[User talk:Mjmohio|talk]]) 19:28, 18 September 2012 (UTC)

{{reflist-talk}}

== External links modified ==

Hello fellow Wikipedians,

I have just modified {{plural:2|one external link|2 external links}} on [[Bisection method]]. Please take a moment to review [https://en.wikipedia.org/w/index.php?diff=prev&oldid=747588430 my edit]. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit [[User:Cyberpower678/FaQs#InternetArchiveBot|this simple FaQ]] for additional information. I made the following changes:

*Added archive https://web.archive.org/web/20130519092250/http://siber.cankaya.edu.tr:80/NumericalComputations/ceng375/node32.html to http://siber.cankaya.edu.tr/NumericalComputations/ceng375/node32.html

*Added archive https://web.archive.org/web/20060901073129/http://numericalmethods.eng.usf.edu/topics/bisection_method.html to http://numericalmethods.eng.usf.edu/topics/bisection_method.html

When you have finished reviewing my changes, please set the ''checked'' parameter below to '''true''' or '''failed''' to let others know (documentation at {{tlx|Sourcecheck}}).

{{sourcecheck|checked=false}}

Cheers.—[[User:InternetArchiveBot|'''<span style="color:darkgrey;font-family:monospace">InternetArchiveBot</span>''']] <span style="color:green;font-family:Rockwell">([[User talk:InternetArchiveBot|Report bug]])</span> 06:01, 3 November 2016 (UTC)

== External links modified ==

Hello fellow Wikipedians,

I have just modified 3 external links on [[Bisection method]]. Please take a moment to review [https://en.wikipedia.org/w/index.php?diff=prev&oldid=791555720 my edit]. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit [[User:Cyberpower678/FaQs#InternetArchiveBot|this simple FaQ]] for additional information. I made the following changes:

*Corrected formatting/usage for http://siber.cankaya.edu.tr/NumericalComputations/ceng375/node32.html

*Added archive https://web.archive.org/web/20090413123941/http://numericalmethods.eng.usf.edu/topics/textbook_index.html to http://numericalmethods.eng.usf.edu/topics/textbook_index.html

*Added archive https://web.archive.org/web/20060906070428/http://numericalmethods.eng.usf.edu/ to http://numericalmethods.eng.usf.edu/

When you have finished reviewing my changes, you may follow the instructions on the template below to fix any issues with the URLs.

{{sourcecheck|checked=false|needhelp=}}

Cheers.—[[User:InternetArchiveBot|'''<span style="color:darkgrey;font-family:monospace">InternetArchiveBot</span>''']] <span style="color:green;font-family:Rockwell">([[User talk:InternetArchiveBot|Report bug]])</span> 01:09, 21 July 2017 (UTC)

== Mathematical formula ==

An anonymous editor made this [https://en.wikipedia.org/w/index.php?title=Bisection_method&curid=646651&diff=990435795&oldid=986016881&diffmode=source] revision to the article. Was this correct? Thanks for your time. [[User:Opalzukor|Opalzukor]] ([[User talk:Opalzukor|talk]]) 13:44, 24 November 2020 (UTC)