Improve matrix multiplication and solvers

[bardo84]

See

https://discourse.julialang.org/t/julia-vs-zig-surprise/74540/11
The Linear Algebra Mapping Problem. Current State of Linear Algebra Languages and Libraries

[antoine-levitt]

Would be good to be clear what exactly is missing. Julia can definitely do diagonal/triangular matrix multiplies, it just wants you to use the appropriate types (ie Diagonal instead of plain matrix). It doesn't try to read off properties from the numerical values of the matrix (eg it won't do anything fancy with diagm), which I think is completely reasonable.

[oscardssmith]

I believe Julia is currently missing optimized Symmetric*Symmetric.

[bardo84]

I have contacted the authors of the paper for input.

[mcabbott]

Table 7: Experiment #6 in the paper is also wrong, for Julia 1.7.

Edit: at last I found it, they specify Julia 1.5.2, thus too old for this.

Their article is "[v2] Sun, 5 Sep 2021" without comment on what changed, perhaps they did not re-run experiments.

[ViralBShah]

May I suggest that we use discourse to zero in on the problems and then open specific issues for each case that are actionable? If folks agree, we can close this issue.

[DilumAluthge]

Alternatively, if you like, we can convert this issue to a GitHub Discussion - just click on the "convert to discussion link", which will close the issue and convert it to a discussion.