Talk:Total variation

Commonly understandable explanation?

I claim to rarely complain, but how can you input 2-3 print pages of formulae without a single commonly understandable definition?!? Thanks in advance to whoever fixes this!Michi zh (talk) 07:51, 26 August 2008 (UTC)[reply]

I added a picture, that may help. Oleg Alexandrov (talk) 04:51, 25 September 2008 (UTC)[reply]

Oleg, I think the image is wrong. The red ball shows the function value, not the total variation. You forgot the absolute value in the integrand. Eli Osherovich (talk) 16:47, 27 September 2008 (UTC)[reply]

Could you explain what is n_p? 87.82.100.74 (talk) 13:15, 22 July 2009 (UTC)[reply]

n_{P}

is simply the number of points of the given partition

P

, as shown in the definition of the set of all partitions

\scriptstyle {\mathcal {P}}=\left\{P=\{x_{0},\dots ,x_{n_{P}}\}|P{\text{ is a partition of }}[a,b]\right\}

of the given interval. Daniele.tampieri (talk) 16:46, 31 July 2010 (UTC)[reply]

My opinion? First equation (image) = first error, so I switched to http://mathworld.wolfram.com/TotalVariation.html . Bye Wikipedia for mathematics. Sad, but true. —Preceding unsigned comment added by 85.222.96.132 (talk) 23:52, 2 September 2009 (UTC)[reply]

About the tagging of the "Total variation of probability measures" section

Years ago, when I started editing this entry, I found that the references dealing with the topic of that section were scarce, and I tried to add remedy the situation by adding the external link to the following paper:

M. Denuit and S. Van Bellegem "On the stop-loss and total variation distances between random sums", discussion paper 0034 of the Statistic Institute of the "Université Catholique de Louvain".

However, anonymous user 128.125.232.122 has pointed out that "That reference was in no way an appropriate reference for the material on this page. Probably just the authors promoting their work." (obviuously, in the light of what I've said previously, the last comment is erroneous), while Melcombe tagged correctly but imprecisely the entry: then I decided to remove that external link and tag precisely the most unreferenced section of the entry, whose topic is also dealt (in the same unreferenced way) in the separated entry "Total variation distance of probability measures", both started by the same wikipedia editor, Michael Hardy. I hope that both Michael Hardy and Melcombe (who also contributed to the entry on that topic) will add more reliable references to improve this and their entry. Daniele.tampieri (talk) 20:46, 25 May 2012 (UTC)[reply]

Missing word

There is a world missing in the definition of the multi dimensional total variation:

the total variation of f in MISSING is defined as

MISSING denotes the place of the missing word. — Preceding unsigned comment added by Cocus (talk • contribs) 13:53, 5 June 2012 (UTC)[reply]

The missing term Ω was added: unfortunately it is not a word, so at first I did not noticed it was missing.Daniele.tampieri (talk) 09:24, 6 June 2012 (UTC)[reply]

Total Variation for Multi Variate Functions

Currently the section "The form of the total variation of a differentiable function of several variables" states the TV as:

$V(f,\Omega )=\int _{\Omega }\left|\nabla f(x)\right|\mathrm {d} x$

It uses the absolute value though the gradient is a vector. It should be replaced with a norm. Royi A (talk) 20:06, 29 December 2023 (UTC)[reply]