... What part of linear algebra isn't computational?
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Computational Linear Algebra
11–20 of 59 posts
Re: Computational Linear Algebra
#12... What part of linear algebra isn't computational?
Many theorems let you know that something exists but don't tell you how to compute it efficiently (an orthogonal basis, eigenvalues, inverses, etc.)
Also, sometimes algorithms can be invented and empirically shown to have good complexity properties before there are proofs.
Re: Computational Linear Algebra
#13Why 'computational' and not 'numerical'?
Re: Computational Linear Algebra
#14... What part of linear algebra isn't computational?
Like... most of it?
You can't do linear algebra "safely" without doing error analysis. So lots of decompositions and operations are very useful for proofs and finding bounds - but can't be use directly to compute values. It's why a good fraction of stuff people do with linear algebra is numerically garbage
Re: Computational Linear Algebra
#15Why 'computational' and not 'numerical'?
Probably to emphasize that it is a practical course. Numerical courses, at least those I've seen or completed, tend to focus on algorithms and their properties, not implementation.
> Jeremy and I developed this material for a numerical linear algebra course we taught in the University of San Francisco’s Masters of Analytics program, and it is the first ever numerical linear algebra course, to our knowledge, to be completely centered around practical applications and to use cutting edge algorithms and tools,
Re: Computational Linear Algebra
#16... What part of linear algebra isn't computational?
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Re: Computational Linear Algebra
#17... What part of linear algebra isn't computational?
I found the part which use Zorn's Lemma pretty un-computational :) It's equivalent to the axiom of choice and is used to show that every vector space has a basis
Re: Computational Linear Algebra
#18I'm excited to do this after I get through as much of the DL course as I can. Maybe that's a bit backwards but whatever.
Thanks for your hard work, Rachel! Really curious what you two will get up to next.
Re: Computational Linear Algebra
#19For someone with an ancient undergrad math background and only "interested observer" level of machine learning knowledge, would it be better to do this course before tackling the deep learning one?
Re: Computational Linear Algebra
#20> Locality: traditional runtime computations focus on Big O, the number of operations computed. However, for modern computing, moving data around in memory can be very time-consuming I need to nitpick here... Big O notation is a way to describe growth rates of functions. You can count data movements (or anything else) with Big O.
Moreover, "moving data around in memory can be very time-consuming" means that in the end, it is still about time, not about memory. So the correct way would be to translate memory access to time, but that means modelling the memory hierarchy, modelling caches in general, and finally perhaps modelling the specifically used caching strategies.
Yes, the memory hierarchy is discussed in the course, and algorithms are shown that are designed to take account of this. Older algorithms tended to only consider computation time, not memory access time.