Dirk T.

Yes gradients are implemented symbollically, see [here](https://github.com/tensorflow/tfjs-core/blob/d29b47a91fd60b627238210722bf801d6556de01/src/ops/linalg_ops.ts#L765-L778). But it requires quite a few new operations (`bandPart`, `triangularSolve`, `setDiag`, ...) to be introduced, which is why the PR became so massive.

> **Updates** > @DirkToewe I took a closer look at your benchmarks. I appear to be using the algorithm from wikipedia? I am using the one mentioned in https://homepages.inf.ed.ac.uk/imurray2/pub/16choldiff/choldiff.pdf, which...

Hi @kedevked, It's awesome that You've started the implementation of some of the most crucial Linear Algebra operations. I'm afraid, however, that the Implementation of the QR ~~Algorithm~~ iteration has...

So You're exporting `eingen` only for testing purposes only? Got it! Point 3 from my bullet points still applies except that You can use a Bi-Diagonal Decomposition instead of Hessenberg.

Sorry to bring this up again but I am still wondering about a few points: 1. I am not sure that the QR *iteration* - even for symmetric positive semidefinite...

QR decomposition, QR iteration and (Francis implictly shifted) QR method, are three distinct algorithms in my understanding (see: Linear Algebra Handbook, chap. 42 "Symmetric Matrix Eigenvalue Techniques"). If I understand...

This is a rabbit hole that will probably lead You to the [Golub-Reinsch algorithm](http://people.duke.edu/~hpgavin/SystemID/References/Golub+Reinsch-NM-1970.pdf) or the [Francis QR algorithm](http://people.inf.ethz.ch/arbenz/ewp/Lnotes/2010/chapter3.pdf) for nonsymmetric Eigen problems. The best shift would be an actual...

For symmetric eigenvalue problems (like the SVD) there is also another, simpler algorithm: The (classic) [Jacobi eigenvalue algorithm](https://en.wikipedia.org/wiki/Jacobi_eigenvalue_algorithm). It also takes O(n⁴) operations and in my opinion it is much...

Waiting for suggestions/requests/review. No more commits will be made until then.

Okay, I will start with adding a special operation. The JDK allows You to do something along the lines of: ```java Pattern.compile("(?i)Hello(?-i)World") ``` Which makes the first part case-insensitive and...