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LinearSolve.jl: High-Performance Unified Interface for Linear Solvers in Julia. Easily switch between factorization and Krylov methods, add preconditioners, and all in one interface.

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Let's see if this solves our problem. It simplifies things, and reaches into internal functions less. I'll investigate UMFPACK as well, I don't remember why we're reaching so deep into...

https://github.com/hypre-space/hypre In particular, [BoomerAMG](https://hypre.readthedocs.io/en/latest/solvers-boomeramg.html) only needs a general sparse matrix, without extra physical knowledge.

I saw in the [docs](https://linearsolve.sciml.ai/stable/) that "the current algorithms should support automatic differentiation," and played around with it a bit. My ultimate goal is to get a Hessian-vector product working...

https://github.com/exanauts/CUSOLVERRF.jl

```julia julia> using LinearSolve, LinearAlgebra; A=rand(4,4); b=rand(4); sol=solve(LinearProblem(A,b),KrylovJL_GMRES()); norm(A*sol.u - b) 2.546262077003306e-15 julia> sol.resid 4 ```

https://github.com/JuliaSmoothOptimizers/HSL.jl

instead of src/preconditioners.jl, use https://github.com/SciML/SciMLOperators.jl

If you're reusing a LinearCache to solve a slightly perturbed system, it would be useful to do a low-rank update on `cacheval` instead of recomputing the factorization? something like a...