Add API to update iterative solver tolerances

[termi-official]

Checklist

• Appropriate tests were added
• Any code changes were done in a way that does not break public API
• All documentation related to code changes were updated
• The new code follows the
  contributor guidelines, in particular the SciML Style Guide and
  COLPRAC.
• Any new documentation only uses public API

Additional context

Add any other context about the problem here.

[termi-official]

There is some issue on master (see e.g. https://github.com/SciML/LinearSolve.jl/actions/runs/19331508201/job/55295492581#step:6:341 ) where the Krylov.jl solvers report that the solve failed, but the solution looks fine, which is unrelated to this PR.

[ChrisRackauckas]

@jClugstor

[jClugstor]

It only hits that message if the retcode is also being set to Failure, which only happens if the solver stats stats.solved is false. So the message is doing what it's supposed to

LinearSolve.jl/src/iterative_wrappers.jl

Line 311 in 5df1b29

stats = @get_cacheval(cache, :KrylovJL_GMRES).stats

[ChrisRackauckas]

Rebase this.

[ChrisRackauckas]

Looks like tests are failing.

[ChrisRackauckas]

is this not supported? Since this is the only one people actually use.

[termi-official]

All Krylov packages are supported. This was was in particular easy, because you pass the tolerance into the solve call. The relevant lines for the transfer are these

LinearSolve.jl/src/iterative_wrappers.jl

Lines 268 to 269 in d53ba71

	atol = float(cache.abstol)
	rtol = float(cache.reltol)

LinearSolve.jl/src/iterative_wrappers.jl

Lines 290 to 291 in d53ba71

	kwargs = (atol = atol, rtol, itmax, verbose = krylovJL_verbose,
	ldiv = true, history = true, alg.kwargs...)

LinearSolve.jl/src/iterative_wrappers.jl

Line 297 in d53ba71

Krylov.krylov_solve!(args...; M, kwargs...)