User talk:Jerzy.Respondek

Managing a conflict of interest

Hello, Jerzy.Respondek. We welcome your contributions, but if you have an external relationship with the people, places or things you have written about on Wikipedia, you may have a conflict of interest (COI). Editors with a conflict of interest may be unduly influenced by their connection to the topic. See the conflict of interest guideline and FAQ for organizations for more information. We ask that you:

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Also, editing for the purpose of advertising, publicising, or promoting anyone or anything is not permitted. Thank you. Jac16888 ^Talk 14:59, 24 June 2022 (UTC)[reply]

Conflict-of-interest editing

Despite the above warning, you did recently conflict-of-interest editing in several Wikipedia articles either by editing your own page, or by adding, in several articles, references to your own work. Please stop using Wikipedia for promoting your own work. D.Lazard (talk) 10:01, 17 December 2024 (UTC)[reply]

Nomination of Jerzy Respondek for deletion

A discussion is taking place as to whether the article Jerzy Respondek, to which you have significantly contributed, is suitable for inclusion in Wikipedia according to Wikipedia's policies and guidelines or if it should be deleted.

The discussion will take place at Wikipedia:Articles for deletion/Jerzy Respondek until a consensus is reached, and anyone, including you, is welcome to contribute to the discussion. Users may edit the article during the discussion, including to improve the article to address concerns raised in the discussion. However, do not remove the article-for-deletion notice from the top of the article.

To customise your preferences for automated AfD notifications for articles to which you've significantly contributed (or to opt-out entirely), please visit the configuration page. Delivered by SDZeroBot (talk) 01:01, 18 December 2024 (UTC)[reply]

Fast Hermite interpolation

To editor Jerzy.Respondek: On Wikipedia:Articles for deletion/Jerzy Respondek you wrote "If there exists another always quadratic algorithm, I would be very curious to get informed of such an ?"

This article-for-deletion page is not the right page for such a question. This the reason for which I answer here. This follows my edit in Vandermonde matrix, where I fixed your wrong assertion "The only existing algorithm for the inverse of the confluent Vandermonde matrix, which works in quadratic time for any parameter series allowed by the definition". In fact, there are several well known algorithms that work in quadratic time, and there are algorithms that work in quasilinear time. This follows form your true assertion that computing the inverse of a confluent Vandermonde matrix is equivalent with solving a problem of Hermite interpolation. In the latter article, I added a section showing that the Chinese remainder theorem provides an easy proof of the existence and uniqueness of Hermite interpolation. Moreover, "Chinese remaindering" can be done by computing greatest common divisors of polynomials. Standard techniques of algorithmics allow showing that, if one uses the Euclidean algorithm, this provides an algorithm for Hermite interpolation that works in quadratic time, and, if one use fast polynomial multiplication in quasilinear time (using Fast Fourier Transform), this provides a quasilinear algoithm for Hermite interpolation and thus for inverting confluent Vandermonde matrices. These are not galactic algorithms, since the use of fast Fourier transform for polynomial multiplication is used in several widely distributed software.

I hope this convince you. D.Lazard (talk) 18:41, 19 December 2024 (UTC)[reply]

For sure it is not quasilinear, due to the simply fact the inversion of a square matrix is also a matrix, thus contain N^2 elements to be calculated. That is possible, and known, but for systems of linear equations with CVM as a system matrix - because we are calculating <N> unknowns. Jerzy.Respondek (talk) 20:36, 19 December 2024 (UTC)[reply]

It is still an interesting case. Indeed, for a given point series rewriting it in a form of Hermite Interpolation (HI) we have exactly the CVM (Spritzbart 1960 page 45). But is the solution of HI also so clearly equivalent to CVM n^2 inversion entries?

I'm not saying no, but what You say would be very interesting (Journal!) article, especially involving FFT. (Disclaimer: also stability tests it should pass; quadratic memory complexity is obvious). I saw usage of FFT in articles of Confluent Vandermonde, but systems of equations - thus with n unknowns. For now, we have a bunch of algorithms for inversion, published quite lately (e.g. in 1998), in most prestigious Journals (e.g. from SIAM series), which does not use FFT and admits of n^3 time. And this is a representative example, not an exception.

It this is not a discussion hereafter but positive ask: if You write such an article, or a code, please let me know and send it. In practice what I meet with, is just "people needed a ready-to-use algorithm for the inversion of confluent Vandermonde matrices which works in quadratic time for any values of the parameters allowed by the definition". And (so far) only I gave them the answer. Jerzy.Respondek (talk) 21:41, 19 December 2024 (UTC)[reply]

Sorry, I misread the sentence. This is true that inverting CVM allows HI, but the convese is not true. However, there are hundreds of research papers on Hilbert interpolation, and I would be surprised if none would have fast algorithms for inverting CVM matrices as a byproduct. This is the reason for not accepting in Wikipedia assertions such as "the only algorithm", "the first algorithm", etc

About implementations: Did you look which algorithms are implemented in the major computer algebra systems (SageMath, Maple, Mathematica, ...)? D.Lazard (talk) 10:24, 20 December 2024 (UTC)[reply]

Dear D.Lazard

I am not opt for using phrase 'the only, the best etc'. It is not elegant and not the style for the public articles (even if true). As I said in different place, I have experience in writing public articles for nation-wide agencies, and also www.onet.pl (unfortunately the last one is already vanished).

Pertaining to HI with byproduct of inversion of CVM-It is surprising, also for me. I will not give names, but even contemporary articles with algorithms written by scientists, which published a few hundred pages monographs on special matrices, thus being best possible specialists, does not give always quadratic algorithms. Read at my review (it is enough to read only excerpt with review of other algorithms):

https://arxiv.org/abs/2407.15696

(By the way: this article is now in a review in a "normal" journal, and - even if the reviews will not require - I shall extend it, giving new applications (I found later)).

The only thing is sure: my article gives concrete algorithm and each time I obtain a mail asking for the next, I provide ready to use C code, compillable in Visual C and GNU C under Linux.

It is peculiar by what euphemisms authors tried to conceal, that their algorithms only sometimes work in quadratic case. E.g. saying "it can be written", but how it is not given. Other peculiar way is to write, that "the formulas in a general case have strange/complicated/awkward" etc forms.

Due to Mathematica/Maple etc, it is not published how they invert it. But to make probable, that they devised quadratic algorithms, they must have specialized command "Invert CVM". There for sure is not a special command to this single operation..You understand on Your own..

In a quarter I expect another article on my results in press agency. I guess it is not typical for mathematicians on wiki, to represent science on an authority level and in press news.

To sum up, let You withdraw the nomination for deletion. Better let us together work how to make it fully professional for wiki standards. Jerzy.Respondek (talk) 17:13, 21 December 2024 (UTC)[reply]