Talk:Quasilinearization

The reviewer has asked for attention of an expert, but not said why. I'll try to guess what is needed (I would classify myself as an expert already in the area, having written one graduate-level textbook in numerical methods).

I am, however, new to Wikipedia so I may very well guess wrong. Here is my guess:

If I were a reader, what I would like to see is an example. I can easily prepare one, either a boundary-value problem for ODEs from the cited (classic) textbook or one from some other source (I'm sure I have one kicking around from my own book or course notes). I shrink a little bit from that because math on Wikipedia is neither LaTeX nor Markdown, it seems to me---the tools for generating math for Wikipedia seem to be lacking, or at least lagging behind. But maybe I just don't know them? How would other people generate a math-heavy example? (Come to think of it, I can use Jupyter Book; kind of like using a cannon to kill a mosquito, though. But it does generate HTML. I wonder if it is compatible with Wikipedia's html? Does anyone know?)

Rob.Corless (talk) 17:07, 6 March 2022 (UTC)

I made some minor changes, procrastinating adding an example. Rob.Corless (talk) 18:17, 6 March 2022 (UTC)

I have added an example. The example is such that anyone "skilled in the art" could reproduce the solution given here (and indeed it's at the level of a textbook exercise). It does not qualify as "original research", therefore. But it's a nice example, and I think I will add it as an exercise to the next edition of my textbook, if I ever get around to writing that.

The purpose of the example was to solidify the abstract notion of linearization. I also experimented with the math markup tools, and I find that the pseudo-LaTeX is acceptable enough. Rob.Corless (talk) 15:56, 8 March 2022 (UTC)

There was an apparent error in the "exact solution" of the example previously included; it was missing a scale factor. This has now been corrected and confirmed by a computation in Maple. Rob.Corless (talk) 14:40, 9 March 2022 (UTC)

The error was in fact only a typo, a missing "6". The exact solution has a scaling symmetry. I have simplified the presented solution and again confirmed the exact solution against numerical solutions. Rob.Corless (talk) 14:54, 9 March 2022 (UTC)

I have added a figure now. The figure was generated in Matlab (as was the Chebyshev spectral solution it displays). It was compared visually with the exact solutions plotted in Maple, and quantitatively at x=0. I am now confident that everything is correct in the example. I now have a comment about reproducibility of examples in Wikipedia. I have written this "old-school" meaning that there are enough details for anyone "skilled in the art" to reproduce this, and have not made my Matlab or Maple scripts available. Since this example is so small, this is probably good enough practice; and I suspect that where reproducibility is an issue, Wikipedia should probably point to primary sources that make efforts to be reproducible, ie provide code and data for inspection.

Rob.Corless (talk) 15:43, 9 March 2022 (UTC)

In response Greenman I will add the reference from the original request at https://en.wikipedia.org/wiki/Wikipedia:Requested_articles/Mathematics#Differential_equations for this article, namely [1], which does indeed mention "Quasilinearization" in its title.

I have attempted to upgrade the article to an "encyclopedic tone". As discussed in [[2]] , however, it's difficult to address the issue of "Submissions should summarise information in secondary, reliable sources and not contain opinions or original research. " I have chosen to retain the example, which is likely the source of the objection, because I think it materially contributes to the understanding of the process being defined, without being original research. Instead, it is only something that someone "skilled in the art" could be expected to construct for themselves in a few minutes.

Rob.Corless (talk) 18:30, 23 July 2022 (UTC)

@Rob.Corless: Welcome to Wikipedia!

Based on an initial reading, this looks like a nice contribution to me. I'll try to help, since I have some experience, but I'm not an expert on Wikipedia norms (I have more experience on Wikiversity). There are probably just some particulars to sort out, and there are various ways to move things along:

• You may want to directly ask for a review from WikiProject Mathematics, by posting on its discussion page.
• If you're not sure about any standard practices, here are a couple of options that might help:
  • Check "featured articles" in mathematics for examples of high-quality articles.
  • Check out the Wikipedia manual of style for mathematics articles, which includes information about including code or pseudocode, and other topics.
• If you're asked to provide more references, then for uncontroversial information, this article in the Encyclopedia of Mathematics may be okay, according to this Wikipedia article on the usage of tertiary sources.
• "There are theorems stating conditions under which one can know ahead of time when the initial approximation is 'sufficiently close'" probably requires a reference, so that it's easily verifiable.
• I suspect that the phrase "seems to be simpler to think about" should probably be taken out, unless you have a reference and say something like "it has been said that..."
• Instead of "For more information about elliptic functions, see..." it may be better to put the reference in a separate section called "Further reading" or "Bibliography."
• Below are a couple Wikipedia articles that already mention quasilinearization (there may be more), but they don't link to an article on the method, since your article hasn't been approved yet! Maybe the need for such links will help your case, although I didn't check whether these articles refer to the same method you're describing or a different method by another name.
  • https://en.wikipedia.org/wiki/Optimal_control
  • Describing_function

I hope some of that helps!

--Greg at Higher Math Help (talk) 23:19, 23 July 2022 (UTC)

Feedback from New Page Review process

I left the following feedback for the creator/future reviewers while reviewing this article: The current version focuses on just one selective use of the approach. To my knowledge it is much, much more general than this article indicates. For instance there are Taylor series expansions used everywhere in science, and linear approximations are heavily used for Optimization and Non-Linear problems. This article needs a much wider context than it currently has. Related, there may well be an article this should be merged into, I am not certain.

Ldm1954 (talk) 19:21, 6 July 2024 (UTC)

No, the scope of the article does seem reasonable; see https://encyclopediaofmath.org/wiki/Quasi-linearization. This article is about a particular technique in the theory of differential equations (and perhaps more generally functional equations) and that technique is apparently known as quasilinearization (it’s probably not a good terminology; blame mathematicians). The methods you mentioned are more broadly called linearization, which is not and shouldn’t be the scope of this article. —- Taku (talk) 19:53, 6 July 2024 (UTC)

(Of course, I am not arguing against expanding the article to include more applications; just saying reasonable. —- Taku (talk) 20:11, 6 July 2024 (UTC))