I have developed a new algorithm for solving quartic equations, which is amazingly accurate and never loses more than 1 digit, compared to what can be
achieved theoretically, based on the given computer architecture's accuracy (e.g. 53 bits mantissa for IEEE 854 arithmetic), and a measure of the
root's sensitivity to numerical perturbations.
The method, on the other hand, is nearly as fast as a plain implementation of the formula for quartic equations and at least 5 to 10 times as fast as
an iterative numerical method.
I have written a paper in LaTeX and am ready for publication. As I am not affilitated to any research institute, I have seen only two choices:
- free publication, but paper is behind a pay wall
- paying for publication, appr. $500 - $1000, depending on the journal
Besides that, the journal also imposes restrictions on the use of the algorithm and the paper I have now, as long as it still is in the peer review
process and also if it indeed is accepted for publication (e.g. I may not put it on my website for free download).
I was thinking, isn't there any form of open science, a little bit like open source software? But now for research papers. I did a search myself and
indeed found some things, but one thing I found requires the research to be funded by some european organisation. I found something else, from some
Pakistani website, but that looked somewhat dubious. I want publication in a decent journal, with a decent review process. Some journals may publish
(e.g. online) yet to be reviewed papers, but then there must be an intent to do the review process. I have seen journals with real bogus (one such
low-quality journal even had a paper from some guy, who claimed to have found a general solution to the quintic algebraic equation with radicals only,
while it already is proved almost 200 years ago that there cannot be such a general solution). I do not want to publish my work in such a dubious
journal.
So, if one of you has good experience with "open science" publication, then I am interested in that. The subject is numerical mathematics, or
mathematics in computer science.Tsjerk - 16-5-2022 at 08:59
woelen, first of all: very respectable you managed to get into this position. You managed to develop something worthy of publishing open source. I
don't understand what you did, but I believe you.
I don't have a solution for your problem though, the only thing I can come up with is publishing it behind a paywall and hope readers are willing to
use sci-hub. At least there is a chance sci-hub could become legal, at least somewhere in the world:
Another option is collaboration with someone in the field who could become second author. You would have to give up single authorship though.
Unless you manage to find someone funding the publication, maybe someone in the field disliking the closeness of "open" source. But you would have to
find that someone.
Edit: What I do know about are instances that prevent scooping, like biorxiv, but that is of little help here.
Edit2: This is the first time I actually hear someone having this problem. Let me have a chat with someone who might know
[Edited on 16-5-2022 by Tsjerk]clearly_not_atara - 16-5-2022 at 10:39
It isn't rare for math to be uploaded to arXiv while still being published in a paywalled journal. If you keep looking for journals, you'll probably
find one that lets you do that.
What you're describing is probably a relatively short paper (just an algorithm which is already shorter than Ferrari's algorithm), so you might want
to look for a journal that offers a "Short Note" kind of publication, where such papers are more likely to be accepted.
But the bottom line is that academics themselves always fret over what journal to submit their work to, and nobody I've ever met, in any field, really
knows immediately where they're going to publish, unless they've just made a huge discovery and will definitely get into Science. You just
have to put in the time and energy to find the right publication, unless you know someone who will do it for you, or substitute money for time and pay
the $2500 or whatever it costs to get into PLoS.woelen - 16-5-2022 at 11:38
The paper is between 15 and 20 pages, I estimate (depending on font and typesetting parameters, used by the journal). The solution is not based on
Ferrari's method (which is known already for 300 years or so), nor on any of the other closely related methods. All of these methods suffer from
numerical issues in many corner cases. The method I have is based on an LDL^t decomposition of a quadratic form, which can be reduced in rank by
solving a depressed cubic equation. This is the crux of the method, the cubic resolvent is a depressed cubic equation, instead of a general one, while
at the same time there also is no need to derive a depressed quartic equation before a cubic resolvent can be obtained. This removes a lot of
numerical issues, due to numerical cancellation.
The paper not only gives an outline of the algorithm, but also contains an error analysis, a description of a test suite, and the results of the test
suite, compared with the theoretical accuracy. Hence the 15-20 pages. If I find the time, and have the motivation for that, then I might try to make
the method even more accurate by using so called fused multiply-add instruction, as available on nearly all modern computer architectures. But in the
current paper I only mention this as a possible research direction, for (slight) improvement.
[Edited on 16-5-22 by woelen]beta4 - 16-5-2022 at 13:05
It's not uncommon to publish a paper behind a paywall and then also upload a preprint on arXiv.
You have to read the fine print of the journal policy to see if it is allowed though.
What is copyrighted is the final version of the paper that has been edited by the journal, and that remains behind a paywall. However, it is usually
allowed to just compile the latex sources of the last version of the paper you submitted for publication and upload that on arXiv. IEEE allows this
for example as long as the version on arXiv includes a notice linking to the doi of the official version of the paper. I've done it myself a number of
times.Dr.Bob - 16-5-2022 at 16:38
Congrats, I am impressed even though I barely understood the method or most of the words used. And to think I used to think of myself as good at
math, but I'm apparently not good at complex math. I was happy to be able to write a formula to determine a right triangle sides from the area and
perimeter in high school/college.
But there are several open source journals in chemistry now, there must be some open source math ones by now, I would think. I would agree that
publishing anywhere is a good start, and often you can get PDFs to share as the author (like on researchgate or other places), plus as stated, many
people use other methods.
Good luck and happy publishing. And remember, at least where I work, if you get published, you need to bring donuts to share. Not sure how to
upload them here, however... Jenks - 17-5-2022 at 08:39
I don't have a solution for your problem though, the only thing I can come up with is publishing it behind a paywall and hope readers are willing to
use sci-hub. At least there is a chance sci-hub could become legal, at least somewhere in the world
This is basically what I did, long ago before sci-hub existed - I published in a pay-walled journal, then took the risk of making my paper available
for download on my own website. So far so good. I only learned about sci-hub just now (thanks Tsjerk) and kick myself that I didn't know sooner.
