Daniel Karrasch

Have you considered `OrdinaryDiffEq.jl` for time-stepping? They have many solvers with adaptivity, and some with GPU-compatibility, though I haven't kept myself up-to-date recently.

I came across this package as I was looking for some "professional" solution instead of my own stupid hack, and it looks really good. It would be great to have...

As long as you get a correct answer, I'm not sure a user would bother whether they would get the same result if they chose a different (i.e. dense) representation....

We have https://github.com/JuliaLang/julia/blob/276af848511510861f8d0e6c1e69e15e4c646e3e/stdlib/LinearAlgebra/src/symmetriceigen.jl#L170-L175 which does exactly what you propose, but the method signature don't lead there for your example. I'll try to come up with some "promotion mechanism" that would...

Actually, can you help me benchmark the `UtiAUi` thing and compare to `rdiv!(ldiv!(U', parent(A)), U)`? I must have made a mistake, but on my machine `UtiAUi!` is not allocation-free, and...

Tests pass locally. It would be great if people could try this on their favorite use cases, and look at precision and performance.

> In particular, it looks like it does eigen of tridiagonal matrices, which is awesome (this comes up all the time for quick & dirty 1D PDE examples) Well, but...

I'm not a native speaker, but shouldn't it be "converse" rather than "inverse" in any case?

I was just thinking that in the context of functions, the inverse function is one that returns the argument to a given outcome of the original function. In this context,...

Creating dense arrays seems a bit wasteful. I think one can do much better in the case when the `Diagonal` is the second argument/rhs, as you say @pcjentsch. I think...