Talk:Borwein's algorithm: Difference between revisions

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Borweins'?

Should this be called Borweins' algorithm, as it belongs to two Borweins? Shreevatsa (talk) 23:25, 28 September 2008 (UTC)[reply]

A quick google books search suggests that "Borwein's algorithm" is an established name for the algorithm. — Carl (CBM · talk) 00:01, 29 September 2008 (UTC)[reply]

Ok then. I see only a handful of results either way (3 for Borwein's and 5 for Borweins', so actually more for the latter) but maybe you searched something else. Regular Google searches give 785 for Borwein's and 117 for Borweins', but it's hard to tell how many of them are authoritative. Anyway I am not myself familiar enough with the literature in this area, so I shouldn't really be talking :) Shreevatsa (talk) 01:01, 29 September 2008 (UTC)[reply]

Error?

I have just programmed the second algorithm (the one with $p_{0}=2+{\sqrt {2}}$ ) into my TI89 Titanium - and it converges to 3.38871193..., not pi. I could not find anything wrong with my program, so something must be wrong with the algorithm. Lucas Brown 42 (talk) 18:45, 27 February 2009 (UTC)[reply]

I have just figured out and corrected the error: the article stated that

x_{0}={\sqrt {2}}

y_{0}={\sqrt[{4}]{2}}

.

This should, and now does, read

x_{0}={\sqrt {2}}

y_{1}={\sqrt[{4}]{2}}

.Lucas Brown 42 (talk) 20:22, 27 February 2009 (UTC)[reply]

Will soon delete sections without citations

I have put citation needed on the different sections. I will search for citations on the web for the separate formulae and try and fill in a few, then if any remain I will remove them in a couple of weeks time. Dmcq (talk) 08:26, 2 June 2011 (UTC)[reply]

Self-correcting algorithms

In the section of the quartic convergence algorithm the article says: The algorithm is not self-correcting; each iteration must be performed with the desired number of correct digits of π.
My question is: does it mean that all the other algorithms in this page are self-correcting (and only this one in particular is not)?--87.5.217.194 (talk) 22:24, 22 February 2012 (UTC)[reply]

Assessment comment

The comment(s) below were originally left at Talk:Borwein's algorithm/Comments, and are posted here for posterity. Following several discussions in past years, these subpages are now deprecated. The comments may be irrelevant or outdated; if so, please feel free to remove this section.

The quartic formula is wrong. It is equivalent to the quadratic formula, but in a slightly different form.

A more complete list of pi formulas can be found in J&J Borwein et.al., The Quest for Pi

67.142.130.33 (talk) 05:58, 11 November 2008 (UTC)[reply]

Last edited at 05:58, 11 November 2008 (UTC). Substituted at 01:49, 5 May 2016 (UTC)

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-{{maths rating|class=Start|importance=Low|field=analysis}}
+{{WikiProject banner shell|class=Start|
+{{WikiProject Mathematics|importance=Low}}
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 == Borweins'? ==
@@ Line 11: / Line 13: @@
 == Error? ==
-I have just programmed the second algorithm (the one with <math>p_0 = \2+sqrt[]2</math>) into my TI89 Titanium - and it converges to 3.38871193..., not pi.  I could not find anything wrong with my program, so something must be wrong with the algorithm.  [[User:Lucas Brown 42|Lucas Brown 42]] ([[User talk:Lucas Brown 42|talk]]) 18:45, 27 February 2009 (UTC)
+I have just programmed the second algorithm (the one with <math>p_0 = 2 + \sqrt2</math>) into my TI89 Titanium - and it converges to 3.38871193..., not pi.  I could not find anything wrong with my program, so something must be wrong with the algorithm.  [[User:Lucas Brown 42|Lucas Brown 42]] ([[User talk:Lucas Brown 42|talk]]) 18:45, 27 February 2009 (UTC)
 :I have just figured out and corrected the error: the article stated that
-::: <math>x_0 = \sqrt[2]2</math>
+::: <math>x_0 = \sqrt2</math>
 ::: <math>y_0 = \sqrt[4]2</math>.
 :This should, and now does, read
-::: <math>x_0 = \sqrt[2]2</math>
+::: <math>x_0 = \sqrt2</math>
-::: <math>y_1 = \sqrt[4]2</math>.  <small><span class="autosigned">—Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[User:Lucas Brown 42|Lucas Brown 42]] ([[User talk:Lucas Brown 42|talk]] • [[Special:Contributions/Lucas Brown 42|contribs]]) 20:19, 27 February 2009 (UTC)</span></small><!-- Template:Unsigned --> <!--Autosigned by SineBot-->
+::: <math>y_1 = \sqrt[4]2</math>.[[User:Lucas Brown 42|Lucas Brown 42]] ([[User talk:Lucas Brown 42|talk]]) 20:22, 27 February 2009 (UTC)
+== Will soon delete sections without citations ==
+I have put citation needed on the different sections. I will search for citations on the web for the separate formulae and try and fill in a few, then if any remain I will remove them in a couple of weeks time. [[User:Dmcq|Dmcq]] ([[User talk:Dmcq|talk]]) 08:26, 2 June 2011 (UTC)
+== Self-correcting algorithms ==
+In the section of the quartic convergence algorithm the article says: ''The algorithm is not self-correcting; each iteration must be performed with the desired number of correct digits of π''.<br />My question is: does it mean that all the other algorithms in this page are self-correcting (and only this one in particular is not)?--[[Special:Contributions/87.5.217.194|87.5.217.194]] ([[User talk:87.5.217.194|talk]]) 22:24, 22 February 2012 (UTC)
+==Assessment comment==
+{{Substituted comment|length=372|lastedit=20081111055801|comment=The quartic formula is wrong. It is equivalent to the quadratic formula, but in a slightly different form.
+A more complete list of pi formulas can be found in J&J Borwein et.al., [http://oldweb.cecm.sfu.ca/personal/jborwein/quest.pdf The Quest for Pi]
+[[Special:Contributions/67.142.130.33|67.142.130.33]] ([[User talk:67.142.130.33|talk]]) 05:58, 11 November 2008 (UTC)}}
+Substituted at 01:49, 5 May 2016 (UTC)