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LU Factorization and Linear Systems for Programers

dragan.rocks

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Re: LU Factorization and Linear Systems for Programers

#5

Post by dagss »

For programmers, the really interesting part of dense linear algebra is how to achieve high performance, as blocking techniques have to be used to amortize loads from memory to cache.

Google for Goto's "Anatomy of high-performance matrix multiplication", one of my favorite programming texts.

Also the papers underlying the development of the "Elemental" library for distributed dense linear algebra is worth a look.

Re: LU Factorization and Linear Systems for Programers

#6

Post by leeoniya »

interactive demo of LU-like and QR-like decomposition of affine matrices:

http://frederic-wang.fr/decomposition-of-2d-transform-matric...

i mostly copy-pasted the js code from this page as a contribution to this lib back in the day: https://github.com/epistemex/transformation-matrix-js

Re: LU Factorization and Linear Systems for Programers

#8

Post by gmiller123456 »

dagss wrote: post #5

For programmers, the really interesting part of dense linear algebra is how to achieve high performance, as blocking techniques have to be used to amortize loads from memory to cache. Google for Goto's "Anatomy of high-performance matrix multiplication", one of my favorite programming texts. Also the papers underlying the development of the "Elemental" library for distributed dense linear algebra is worth a look.

To save people a few clicks:

[1] https://www.cs.utexas.edu/users/pingali/CS378/2008sp/papers/...

Re: LU Factorization and Linear Systems for Programers

#9

Post by stephencanon »

hprotagonist wrote: post #3

Golub's "Matrix Computations" remains a must-read reference text here: http://web.mit.edu/ehliu/Public/sclark/Golub%20G.H.,%20Van%2...

Do note that Golub & Van Loan is very much a reference text, however; it is not a great choice if you're just learning the subject (it covers everything, but without much depth and without much exposition).

Re: LU Factorization and Linear Systems for Programers

#10

Post by FabHK »

dagss wrote: post #5

For programmers, the really interesting part of dense linear algebra is how to achieve high performance, as blocking techniques have to be used to amortize loads from memory to cache. Google for Goto's "Anatomy of high-performance matrix multiplication", one of my favorite programming texts. Also the papers underlying the development of the "Elemental" library for distributed dense linear algebra is worth a look.

> how to achieve high performance

You really just want to use LAPACK/BLAS, no? (That's what the Neanderthal library mentioned in the article does, btw, and basically linear algebra libraries for other languages, too. If not, you probably shouldn't use it...)

http://neanderthal.uncomplicate.org

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