User talk:Shawsa7

Welcome!

Hello, Shawsa7! Welcome to Wikipedia! Thank you for your contributions. You may benefit from following some of the links below, which will help you get the most out of Wikipedia. If you have any questions you can ask me on my talk page, or place {{helpme}} on your talk page and ask your question there. Please remember to sign your name on talk pages by clicking or by typing four tildes "~~~~"; this will automatically produce your name and the date. If you are already excited about Wikipedia, you might want to consider being "adopted" by a more experienced editor or joining a WikiProject to collaborate with others in creating and improving articles of your interest. Click here for a directory of all the WikiProjects. Finally, please do your best to always fill in the edit summary field when making edits to pages. Happy editing! — Masum Ibn Musa  Conversation 11:41, 5 April 2019 (UTC) Getting Started Contributing to Wikipedia • Tutorial • Your first article The five pillars of Wikipedia • Simplified ruleset How to: edit a page • upload an image Getting Help Frequently Asked Questions Directories and indexes Where to: ask questions • make requests Tip of the day Request administrator attention Policies and Guidelines Neutral point of view • Reliable sources Verifiability • Citing sources • No original research What Wikipedia is not • Biographies of living persons Manual of Style (Simplified) • Three-revert rule Copyrights • Non-free content • Image use policy External links • Spam • Vandalism • Sock puppetry Deletion policy • Conflict of interest • Notability The Community Community Portal • Adopt-a-user program Assume good faith • Civility • Etiquette No personal attacks • Resolving disputes Build consensus • Village pump IRC channels • Mailing lists The Signpost (Wikipedia's newspaper) Things to do Be bold in editing • Help develop an article Maintenance • Peer review • Requested articles Join a WikiProject • Translating articles Cleaning up: General • Spam • Vandalism Miscellaneous Categories • Disambiguity • Stubs User pages • Talk pages Useful templates • Tools • User scripts

RBFs and completely monotone functions

Hi, I notice in your page about RBF interpolation that you wrote: "It has been shown that any function that is completely monotone will have this property, including the Gaussian, inverse quadratic, and inverse multiquadric functions."

I found this confusing because the first example (the Gaussian) is not completely monotone.

A bit of reading suggests that there is a change of variables involved in transforming the Gaussian into a completely monotone function—the Gaussian is positive definite and radial, while the transformed version is completely monotone. The texts I found online refer to sigma and r, where r = sqrt(sigma).

I'm not a mathematician so I'm on shaky ground here and don't think I should correct the page. Maybe you can verify what I found and make your own corrections, if indeed they're necessary? Thanks. Theoh (talk) 14:28, 8 August 2021 (UTC)

Hi Theoh! Good catch! You're absolutely right. The key property is strict positive definiteness as discussed in the citation (Fasshaur 2007). I've updated the page accordingly. I'm not very active on Wikipedia these days, and my research interests have shifted so I'm not actively working with RBFs at the moment. It sounds like you've done your research, so I would encourage you to make edits and contribute to the page. In particular, you could explain the connection to completely monotone functions now that there is no mention of it on the page. If there is anything you're uncertain about, feel free to start a discussion on the talk page or reach out to me again. Shawsa7 (talk) 01:15, 9 August 2021 (UTC)