Dr. Driscoll, thanks for sharing all these videos. I'm studying for my numerical linear algebra final and it's nice to see the material from a different angle. Just wanted to let you know it's very appreciated.
@nUrnxvmhTEuU4 жыл бұрын
11:26 > “So we'll talk more about this convergence rate and what it means.” > end of the video > last video of the series > 😓️
@TobyDriscoll4 жыл бұрын
¯\_(ツ)_/¯
@pilot6154 ай бұрын
Okay, I understood the QR factorization :) Thank You!
@ericchristoffersen93553 жыл бұрын
Lovely lecture. I was implementing a linear solver for fun to develop my intuition for linear programming and was totally stunned when came across the qr iteration. I feel so very far from being able to sympathize with the inventor of the approach - it is like magic and so fascinating. I would love to see your next lecture about why the iteration converges so quickly and hopefully the cases where it wont. I'd also really love a lecture about what can be done to manage floating point precision for those difficult cases. Thanks so much!
@directx872 Жыл бұрын
Converges like magic❤
@texasgoat2991 Жыл бұрын
great video, thanks for sharing
@senhajirhazihamza77187 жыл бұрын
thank you really well explained
@dursundurmaz9155 жыл бұрын
i guess this is our hw answer, thanks alot:)
@Tyokok3 жыл бұрын
Thanks for the great video! One question would you also get EigenVector here? Or is there any other way?
@turuus52152 жыл бұрын
Hey, Tony. Could you help me, pls? I saw your comments in another tutorial.
@Tyokok2 жыл бұрын
what's the question? which comment? I have question here too unanswered yet.
@holyshit9223 жыл бұрын
He didn't mention about shifts and the strategies for choosing shift well
@TobyDriscoll3 жыл бұрын
This is an intro lecture. You should be able now to read Trefethen and Bau's explanation of shifts.
@paulliao16265 жыл бұрын
Thank you very much for sharing. May I ask a question? How do I get the eigenvector after getting the eigenvalue of QR iteration?
@TobyDriscoll5 жыл бұрын
If it's a single eigenvector or a few, you might use inverse iteration. If you want them all, then you have to sort of accumulate the Q matrices as you go.
@turuus52152 жыл бұрын
@@TobyDriscoll Hello, Toby. By chance, do you have Java source code for both eigenvalues and eigen vectors?
@knobberschrabser4244 жыл бұрын
Am I right that you won't get to complex eigenvalues of a real matrix with this algorithm?
@TobyDriscoll4 жыл бұрын
You can introduce a complex shift based on the lower right 2x2 block. But traditionally the target is a "real Schur form," which is not quite triangular. See Golub and Van Loan, for example.
@greensong67245 жыл бұрын
How do you determine how many iterations you gonna use?
@TobyDriscoll5 жыл бұрын
You don't know in advance. You have to monitor the sizes of the off-diagonal elements to know when you've isolated an eigenvalue