Randomized Singular Value Decomposition (SVD)

[@user-hl5sk1oj1m]

I can't believe that I understood this. Thank you so much Prof.

[@chrisw3327]

Thanks Steve!!!! This is a very important approach for my desire to analyse high resolution climate model data.

[@chienthan12345]

Very easy to understand by watching your explanation. Thank you

[@johnl4885]

Good explanation.... not clear why it works as well as it does. Gives us some homework to get to the bottom of these ideas. Thank you

[@nazniamul]

Dear Prof. Your videos are fantastic and help me a lot. I just want to request you to explain (or give the numerical proof) how Sigma and V of Y matrix should be same as original data matrix X. Is there any references or documents I can go through? Your response would be a great help for all of us.

[@zelexi]

this is a fantastic explanation

[@dragosmanailoiu9544]

This prof is cool he’s interested in complex systems and fractals

[@zoloojagaa9198]

Thank you. You just saved my life

[@andrezabona3518]

You are the best! I love your videos!!

[@mahan1598]

Thank you Steve! I have a question: Suppose we have the SVD od the current matrix A. If we add a new snapshot, is there any quick way to find the SVD of the new matrix? It will be useful when we want to find the POD of time-consuming LES or DNS simulations while calculating the flow field.

[@MohammedFarag81]

Thanks for this interesting explanation. I have one question: How do you determine the rank r which requires pre-knowledge of the optimal threshold obtained from the Sigma matrix we are trying to compute using the rSVD? has this point been raised in related work in the literature?

[@nami1540]

Watch the videos before this one in the series

[@Falangaz]

Thanks Prof!

[@MoeGamm]

Great!

[@brunoisy]

Why must the projection be random? From what distribution should it be generated? Couldn't I use the same projection over and over again, which means it wouldn't actually be random?

[@Eigensteve]

In principle, you could pregenerate a big random matrix and then use it over and over. Eventually, you might run into some bias problems, but it should be okay. For example, if I built a camera on these principles, my guess is that my random measurement matrix C might not change... but that would be fine, since it is highly unlikely that it would be a "bad" matrix for any real-world signals.

[@ondrejkotaba]

Thanks!

[@yasserothman4023]

Thank you. but can you point out how can we compute the SVD using the QR algorithm ? i am referring to @5:29

[@karthikr3977]

kool stuff]

[@butette]

Stupid question but what is the system you use to write on the screen like that? It looks very cool.

[@nazniamul]

He use a transparent glass as a writing board and keep the background dark. Then mirror the whole video so that we can see the transformed version of whole activities. You can imagine the whole process as a transformation of space (or matrix manipulation). The whole idea is just amazing.

[@Erotemic]

I realize it's postprocessing but it bugs me that it looks like his writing appears backwards from his perspective.

[@mahan1598]

Look at his ring on his right hand! It is revered!

[@nami1540]

But what is Q and R? You never explained ...

[@cretinobambino]

Look for QR decomposition in your favorite linear algebra book.