Preconditioned Conjugate Gradient Descent (ILU)

[@graphicsRat]

Simple, clear. I love it. I want more. A whole series on optimization.

[@mkelly66]

All of your videos did a great job of clearly explaining the topics. Thanks, I really appreciated the clear explanations!

[@QT-yt4db]

The dog at the end is lovely...

[@MrFawkez]

A great followup to the CG video. Thank you.

[@swaggcam412]

This is a great resource, thank you for sharing!

[@xplorethings]

Really well done!

[@colin_hart]

Thank you for creating this presentation. I arrived here while looking for exposition on Arnoldi and Lanczos iteration. Any new content about sparse iterative methods would be gratefully received. Cheers!

[@dmit10]

I would suggest L-BFGS, partial Cholesky decomposition (version with limited memory), and "when to use proximal methods over non-proximal" (not just how they work).

[@ricardomilos9404]

In this video was shown that the A^-1 ≈ L^-1U^-1 = M. In code was used M^-1 = L * U (element wise multiplication of LU, not matrix multiplication). It follows that preconditioning only requires the diagonal of the matrix U, since everything else is reduced Should elementwise multiplication be implemented instead of matrix multiplication? And is it correct that M^-1 = LU (maybe it should be like this M^-1 = L^-1U^-1 ?)

[@PriyaDeo]

Please note that A^-1 ≈ U^-1L^-1 (not L^-1U^-1), since we are taking the LU factorization of matrix A : A ≈ LU => A^-1 = (LU)^-1 => A^-1 = U^-1L^-1. In the code, we did do matrix multiplication. The numpy matrix library uses '*' to denote matrix multiplication. For element-wise multiplication you need to use np.multiply(L, U).

[@QT-yt4db]

Great video, but the voice is a little bit low, makes it hard to hear without turning high the volume...

[@Darkev77]

Proximal GD next?

[@nickp7526]

Great stuff! What range of subjects can you cover?

[@nickp7526]

Oh, I just got to the end :) Do you know anything about support vector machines? I have a class on it this semester and I would like a small introduction

[@PriyaDeo]

I have approximate knowledge of many things :P But to answer this question properly: topics from most college-level undergrad courses in Maths & Computer science. Some topics from grad-level courses in Machine Learning, Computer Vision & Robotics. Software Engineering Interview problems (e.g. HackerRank questions). And so on. I can definitely do a video on SVM's.

[@darasingh8937]

Thank you so much!!