@Lepidopterist When you ask it there, you should make it clear what is changing for us to consider convergence/what is happening asymptotically (e.g. is $x$ growing? Then A must change ... so it's not clear how we can even speak of "the trace" of something that's changing. How does that all work? You'd have to set this up carefully for the question to make sense)

@MatthewDrury Aren't there already good linear algebra libraries for C? I'm not really up on the C scene, but my (possibly naive) understanding was that these days this is a well-trodden field.

Is there some way in which existing libraries are not adequate or otherwise undesirable in some manner?

i.e. is there a problem with the current state of affairs that you're solving, or is this more "out of interest", where it doesn't matter so much what's already there?

Thanks @Glen_b, I have clarified the context of my question here: math.stackexchange.com/questions/1467806/…

@Glen_b Oh yah, there certainly are much better offerings than anything I could cook up. This is just for fun, hobby project.

@Lepidopterist Yes, that looks substantially more precise.

@Matt Oh, then that sounds cool.

I spend a lot of time programming in high level languages at work, I've recently got more interested in what happens at a lower level.

@Glen_b Yah, it's fun. I enjoy programming a lot.

@Matt Are you working from some text?

@Glen_b For C, I mostly learned from Learn C the hard way and studying the python interpreter source code.

e.g. something like Golub and van Loan, say?

For the math stuff, I learned the abstract side of it in school, but I don't really have a reference for the computational stuff.

Ill google that!

I mean in terms of what kinds of algorithms you're using in your functions and so on

Seems I'm one message behind each time

@Glen_b Would you recommend this book?

It's one of several books it's probably worth reading.

Ill try to get my hands on a copy.

There's a bunch of neat algorithms for stuff like updating decompositions

eg updating Cholesky or QR decompositions via Givens rotations or Householder transforms

(e.g. when you add variables)

Thats definitely stuff I'm interested in learning about, so I will have to check it out.

It's not necessarily all in that book, though.

Right now my qr is just ghram-shmidt

I learned quite a bit from reading the documentation for linpack many many years back.

Ah.

Thats a good idea as well. I've found you can learn a surprising amount by reading code and code comments.

The comments at the top of some of teh functions were enlightening for me.

They explained what was going on in enough detail that I could figure out the ideas

It led to me being able to help a colleague vastly improve the speed of his MCMC regression code when he was doing his PhD, because he didn't need to compute decompositions every time he had a new model, just update or downdate the change from the last one

That's very cool.

He was doing Cholesky, but the same ideas carry over.

There are a few texts that discuss ideas like those. Golub and van Loan is one that I can remember right now.

Ive been able to use the same notions to speed up other projects as well.

It's really remarkable how little bits of knowledge you pick up can be useful over and over.

But one project also involved changing weights to observations one at a time; I was able to adapt observation-updating/downdating to that part.

That's less numerically stable though, so periodically we recompute from scratch.

There are plenty of times i've learned something that was not obviously useful at the time, and then it has turned out to come in handy multiple times.

Yeah.

Did you pick up stability and floating point knowledge and intuition in the same way?

Iv'e never really felt enlightened about floating point stuff.

That's partly from reading the texts and documentation that I learned the algorithms from

(and partly from experience in some cases.)

Yah, I'm hoping one day those things clarify in my mind.

I have several Numerical Analysis subjects in my past that help.

At least with parts of it

Yah, if I had supernatural foresight I would have taken some classes about these things in school.

Well, I have to give a talk tomorrow, which means I need to get a haircut tonight : )

I better be off before the place closes.

I just did a whole bunch of stuff and ended up using essentially all of it. Makes me wonder what else I might have used.

Okay bye.

Good luck with the talk

@quit

I studied Riemannian Manifolds, which has not yet been useful in my working life.

Oh, wrong forum for that command

One day...

Thanks Glen.

:wq

@AndreSilva: I don't notice any difference in either the vote arrows or the accepted answer ticks. Does anyone else?

@AndreSilva: I was wondering about the same thing. No difference that I can see. Perhaps we should ping @AnnaLear and ask about this mysterious [status-completed] -- probably leaving a comment there is a right venue.

I left a comment to her there. Feel free to complement it. Tks for the feedback. (@Scortchi, @amoeba)

Alright, Anna answered us. She meant to edit another post. Now that status of the post is opened again.

@MatthewDrury I did research in Riemannian manifolds, contact geometry, and Lie Algebras. Although I haven't used any of the advanced stuff as a consultant, both the abstract concepts and the methods of thought, analysis, and exposition these studies instilled in me have always been useful.

@whuber That is absolutely true. Even thought he specific topics I studied in mathematics have not come much in handy, the thought process that you learn studying mathematics are very general and powerful. It comes up in every part of my life.

I feel that even my writing is stronger for having studied mathematics, as you must learn to speak precisely and unambiuously.