Applied Linear Algebra GMRES

[@kolbstar]

I watched this video when I was learning about GMRES a couple years ago, and I wanted to say one thing I wish this video had had in it was a walk through through why GMRES is lower O-complexity than direct solvers. Without some context for things like A being sparse, and how GMRES allows us to always use either dense vectors or sparse matrices, without ever needing to operate on a dense m-by-m, I was a little lost. For example, GMRES looked like it did dozens of O(m^3) operations and yet was faster than a direct solver doing one O(m^3) operation. Like when representing the Krylov subspace, I saw n A^i matrices, and was scratching my head as to how computing those alone could possibly be faster than LU decomposition on A. But then realizing they're just n matrix-vector operations with n

[@yuwuxiong1165]

The insight about the progress in terms of matrix size from 1950 to present is gold!

[@ahmedsheta3104]

If I get a good mark in my oral exam. It’s all thanks to you. Thank you!!

[@GBabuu]

One of the best instructors that I ever came across. Happy subscriber here!!!

[@yinze425]

GMRES is started from 13:30

[@潘启儒]

THX

[@JuanGarcia-lo2el]

I'm enjoying your class!!!!

[@shayanhashemi8327]

such a great prof! good for his students!

[@chainemusique1792]

Thank you so much !!!! My teacher only gave me the algorithm and knowing a little bit where it came from help a lot

[@nadeemahmed2464]

Two books mentioned for iterative solvers, can someone please write the name of those books?

[@prakashnainwal6890]

It's a wonderful lecture. thanks for that. Could anyone please tell me the name of the book suggested for iterative methods other than Trefethen?

[@sparse-manatee]

Very nice. So clear.

[@mahanmehravard5058]

The if I may say "cute" laughs in the middle of the serious mathematical argument are brilliant.

[@minsullee8289]

Thank you! It is really helpful!

[@AJ-et3vf]

Awesome video sir! Thank you!

[@xyw8383]

Amazing, love it!

[@Doomseraph]

Thank you!