A worthwhile OT. Maybe you could submit it as a link?
I want to write some examples (as long blog posts or similar) in a few concrete science fields showing how to use these tools in practice and submit those. I feel like the chebfun guys haven’t really figured out some good introductory hooks yet, or done much marketing/outreach: most of their output is papers about approximation theory which takes some amount of effort to figure out and only get seen by academics working in the same subfield, and the practical examples on their site are pretty small pieces (and don’t have comparisons vs. alternative approaches) so it’s hard to see the big picture. Those lecture videos are pretty good, but an hour long lecture is a somewhat big commitment and hard to skim.
BTW, I’m serious about the email thing: shoot me a note (address in my profile) and I’d love to hear about your attempts to implement Geometric Algebra in code. One of my goals for the next few years is to at some point sit down and write a nice web-based introduction to GA filled with interactive diagrams.
http://www.chebfun.org
Here are a couple of hour-long lecture videos https://www.youtube.com/watch?v=cQp-kB9EOQs http://downloads.sms.cam.ac.uk/1160831/1160835.mp4 and the first 6 chapters of a book explaining the basics of the underlying theory are freely available online (the rest of the book is great too) http://www.chebfun.org/ATAP/
Basic concept is to approximate functions as high-degree polynomials, to within machine precision, and then do operations on those approximations instead of on the original functions, at each step chucking out any coefficients which are smaller than machine precision. This in many cases provides a dramatic speed boost over existing methods for taking integrals/derivatives, finding roots, solving differential equations, convolution, etc. etc., while staying extremely accurate, much better than discrete solutions.
It’s not universally applicable to all functions (for obvious reasons) or all problems, but the team responsible has really done an incredible amount of solid work on the project.
Apparently it’s 10+ years old now, but nobody I’ve asked has ever heard of it before. Which is kind of surprising, because it seems amazing to me so far.
Unfortunately stuck as a Matlab library for the moment (there are partial ports to NumPy and Julia but they are very feature poor compared to the Matlab version).