QR algorithm for eigenvalues

[@johnjasa]

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.

[@nUrnxvmhTEuU]

11:26 > “So we'll talk more about this convergence rate and what it means.” > end of the video > last video of the series > 😓️

[@TobyDriscoll]

¯\_(ツ)_/¯

[@pilot615]

Okay, I understood the QR factorization :) Thank You!

[@ericchristoffersen9355]

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]

Converges like magic❤

[@texasgoat2991]

great video, thanks for sharing

[@senhajirhazihamza7718]

thank you really well explained

[@dursundurmaz915]

i guess this is our hw answer, thanks alot:)

[@Tyokok]

Thanks for the great video! One question would you also get EigenVector here? Or is there any other way?

[@turuus5215]

Hey, Tony. Could you help me, pls? I saw your comments in another tutorial.

[@Tyokok]

what's the question? which comment? I have question here too unanswered yet.

[@holyshit922]

He didn't mention about shifts and the strategies for choosing shift well

[@TobyDriscoll]

This is an intro lecture. You should be able now to read Trefethen and Bau's explanation of shifts.

[@paulliao1626]

Thank you very much for sharing. May I ask a question? How do I get the eigenvector after getting the eigenvalue of QR iteration?

[@TobyDriscoll]

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.

[@turuus5215]

@@TobyDriscoll Hello, Toby. By chance, do you have Java source code for both eigenvalues and eigen vectors?

[@knobberschrabser424]

Am I right that you won't get to complex eigenvalues of a real matrix with this algorithm?

[@TobyDriscoll]

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.

[@greensong6724]

How do you determine how many iterations you gonna use?

[@TobyDriscoll]

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