Talk:Pivot element

Problem in article
I've noticed that someone edited the examples section, and it seems there's at least one problem with it.

Irrelevant to the question if the computation is correct there are 5 digits in the answer of 4 digits precision computation. Clearly it's wrong.

Previously I've computed the example with 4 digits precision and got results which are different from the ones that are currently specified.

It's possible that my computation is wrong, but let's play it fair and post here the computations in order to see who is correct.

Storing precision is 4 digits (of precision), but operations themselves can be performed in higher precision (I don't want to be algorithm dependent).

$$\begin{align} & 0.003000x+59.14y=59.17 \\ & 5.291x-6.130y=46.78 \\ & \text{Forward elimination}\Rightarrow \\ & -6.130-\frac{5.291}{0.003}59.14=-6.130-1764\cdot 59.14=-6.130-1043=-1049 \\ & 46.78-\frac{5.291}{0.003}59.17=46.78-1764\cdot 59.17=46.78-1044=-997.2 \\ & \text{Back substitution}\Rightarrow \\ & y=\frac{-997.2}{-1049}=0.9506 \\ & x=\frac{59.17-56.22}{0.003}=\frac{2.95}{0.003}=983.3 \\ \end{align}$$

--Max (talk) 18:05, 26 October 2010 (UTC)

Another problem: The product of 1764 and 59.14 is not 1043; it's 104300. Similar errors have been made elsewhere. Here's a corrected version $$\begin{align} & 0.003000x+59.14y=59.17 \\ & 5.291x-6.130y=46.78 \\ & \text{Forward elimination}\Rightarrow \\ & -6.130-\frac{5.291}{0.003}59.14=-6.130-1764\cdot 59.14=-6.130-104300=-104300 \\ & 46.78-\frac{5.291}{0.003}59.17=46.78-1764\cdot 59.17=46.78-104400=-104400 \\ & \text{Back substitution}\Rightarrow \\ & y=\frac{-104400}{-104300}= 1.001 \\ & x=\frac{59.17-59.20}{0.003}=\frac{0.03}{0.003}=10 \\ \end{align}$$ — Preceding unsigned comment added by Nm160111 (talk • contribs) 01:08, 9 November 2012 (UTC)


 * The computation must be done in 4 digit arithmetic. The value 104300 is 6 digits long, so the correct value to use is 1043. Maizensh (talk) 04:53, 24 January 2023 (UTC)

Importance
I'm very much not a deletionist, but I look at this page and wonder why these different types of pivoting have been lumped together. Is there something inherent about pivoting that justifies its own page? Personally, I don't see it, but I could be wrong. &mdash; MaxEnt 22:24, 22 August 2020 (UTC)