Update LinearSolve requirement from 2.36.0, 3.7.1,4 to 2.36.0, 3.7.1,4, 5.0

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Updates the requirements on LinearSolve to permit the latest version.

Release notes

Sourced from LinearSolve's releases.

v5.0.0

LinearSolve v5.0.0

Diff since v3.86.1

Breaking changes

1. Reading .cache off the return of solve!/solve no longer works — it is always nothing.
   • Affected downstream: OrdinaryDiffEq (threads linres.cache through chained solves in 6 files) — a parallel PR migrates it off the pattern and must merge before 5.0 releases. NonlinearSolve reads only .u/.retcode and is unaffected (verified below). LinearSolve internals never read sol.cache.
   • Migration: keep the LinearCache you called solve! on:

     # before                                   # after
     sol = solve!(cache)                        sol = solve!(cache)
     linsolve = sol.cache                       linsolve = cache

     For one-shot solve(prob, alg) where you previously continued via sol.cache, switch to cache = init(prob, alg); sol = solve!(cache).
2. cleanup_petsc_cache!(sol::LinearSolution), cleanup_mumps_cache!(sol::LinearSolution), cleanup_superludist_cache!(sol::LinearSolution) methods are removed (they read sol.cache.cacheval). Use the LinearCache methods from an init/solve! cycle: cleanup_*_cache!(cache). GC finalizers remain as the safety net for one-shot solve(prob, alg). Docstrings, docs pages, and the extension test suites are migrated accordingly.
3. Sublibrary/test compat bumps: LinearSolve = "5" in lib/LinearSolveAutotune (→ 1.13.0), lib/LinearSolvePyAMG (→ 1.3.0), docs/, and all test/*/Project.toml.

Merged pull requests:

• QA: run_qa v1.6 form + ExplicitImports (root + sublibs) (#1059) (@​ChrisRackauckas-Claude)
• Use separate cache flags for A and b in ForwardDiff extension (rebased #1054 + test) (#1062) (@​ChrisRackauckas-Claude)
• Improve ForwardDiff sparse matrix specialization and add tests (#1063) (@​hersle)
• Cache inner LinearCache in DualLinearCache in direct dual path (#1065) (@​hersle)
• docs: document symbolic factorization reuse for sparse matrices (#1060) (#1067) (@​ChrisRackauckas-Claude)
• Fix Downgrade: raise MKL_jll compat floor to 2022.2 (#1068) (@​ChrisRackauckas-Claude)
• Route duals-in-b PureKLU solves to a native LinearCache (uses PureKLU 1.1 mixed ldiv!) (#1069) (@​ChrisRackauckas-Claude)
• Add EigenvalueProblem support with dense, Arpack, ArnoldiMethod, KrylovKit, and JacobiDavidson backends (#1071) (@​AJ0070)
• Batched (matrix) right-hand sides: LinearProblem(A, B) ≡ A \ B (v4.0.0) (#1072) (@​ChrisRackauckas-Claude)
• Fix PureKLU Dual-A dispatch stolen by DualBLinearProblem opt-out (#1073) (@​ChrisRackauckas-Claude)
• Batched RHS via Krylov.jl block methods (GMRES/MINRES) (#1074) (@​ChrisRackauckas-Claude)
• Fix dense LU cache prototypes for wrapper matrices (#1076) (@​ChrisRackauckas)
• Document public API coverage (#1077) (@​ChrisRackauckas-Claude)
• GESVFactorization + dense LU pivot-buffer reuse (v4.2.0) (#1078) (@​ChrisRackauckas-Claude)
• Bump version to 4.2.1 (#1079) (@​ChrisRackauckas)
• ci: use targeted monorepo TagBot (#1080) (@​ChrisRackauckas-Claude)
• Qualify issuccess as LinearAlgebra.issuccess to fix QA ExplicitImports failure (#1081) (@​ChrisRackauckas-Claude)
• Complete allocation-free dense LU refactorization: generic-kernel pivot reuse + regression tests (#1082) (@​ChrisRackauckas-Claude)
• LinearSolve 5.0: lightweight solutions — stop populating LinearSolution.cache in solve! returns (#1083) (@​ChrisRackauckas-Claude)
• Fix singular handling in the StaticArrays square fast path with SVD rescue for the default (#1085) (@​ChrisRackauckas-Claude)

Closed issues:

• Batch mode (#552)
• ForwardDiff autodiff with PureKLUFactorization is very slow through implicit ODE solver (#1064)
• LinearSolve v3.85.2+ broke dense implicit ODE solves with ComponentArray u0 (#1075)
• Static LU path returns retcode Success with Inf/NaN solution on singular SMatrix (#1084)

Commits

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[j-fu]

done in #81

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