Power Method with Inverse & Rayleigh

Chapters
0:00 Title Card
0:12 Terminology
0:37 Eigenvalue Example
1:04 Power Method
1:29 Power Method Example
2:33 Notes on Power Method
2:50 Inverse Power Method
3:21 Inverse Power Method Example
4:12 Rayleigh Quotient
4:54 Solve using Determinant
5:15 Inverse Power Method with Shift
5:34 Inverse Power Method with Shift Example
6:12 Rayleigh Quotient Iteration
6:37 Summary
7:01 Thank You

#PowerMethod #RayleighQuotient #NumericalAnalysis

[TuemmlerTanne]

Just found your channel. Great content, abolutely love it! I was completely baffled by that golden ratio eigenvalue for a moment haha, keep it up!

[dantefox]

Wow, you taught me more in 7 minutes then I learned in 2 hours lecture... Like why did my proffesor feel the need to overcomplicate things so much. Amazing video!

[atharvasinnarkar]

dude this covers 4 lectures from trefethen bau ....covered in just 7 mins...amazing stuff!

[fedorpashin]

Thank you very much! Finally understood how to implement the inverse power method.

[bheeshmayo]

You are the best 😭😭😭😭. Your teaching is such a spoon feeding. It helped me a lot thank u .

[hoshizora]

Thank you so much, found this video after browsing for quite a while. Helped a lot

[iulianabinzar]

Thank you from the bottom of my heart!

[yavorpetrov]

Great video, man! It helped me a lot! Wish you all the best!

[ДимаКоролев-ую]

Thank you a lot! Your video very helped me!

[KierkegaardEnjoyer]

I thought normalizing meant to take the sum of squares, not taking the maximum of the two vector elements?

[Palmer]

.75 speed and he sounds just like Toby from the Office

[jjschnyder]

How does the norm yield the maximum of the vector? Are you using the infinity norm?

[nmana]

4:06 i don't understand, why did you factorize out the smaller element -0.6, i thought the norm supposed to be the maximum value from the resulting vector which is 1 ??

[nmana]

please make a video on schur decomposition

[GP-zkfz]

What would be the terminating condition for the Inverse Power Method? Picking infinity norm(bk+1 - bk) does not seem to suffice for our example demonstrating the inverse power method.

[PeterKeynes]

When at 5:31 you mentioned inverse power method can be used to compute eigenvector given eigenvalue. Can you elaborate on how that can be done? I cannot find any readings on this. Thanks!

[ahmedatta]

great video, I have question when you know that u reach to highest eigenvalue or how we convergence? for example why u not complete after 8 iteration in first example

[alexandrevachon]

What happens if I use in the Rayleigh Quotient Iteration, instead of the inverse iteration, but the normal Power iteration?

[thebigmonstaandy]

how do you calculate IIA*b_kII? is it Maximum Norm =biggest absolute Value or just biggest Value?Somepeople calculate IIA*b_kII as 2Norm.is it wright?

[ryanjacksonx]

It's not 100% clear, but I think one must be consistent in the manner of normalization.