Phase 3 — preconditioned iterative solvers + NEFF cache reuse

[scttfrdmn]

Roadmap phase tracker

This issue tracks trnsolver's work on Phase 3 of the trnsci roadmap.

See the suite-level roadmap
for the full phase matrix and cross-project dependencies. A reader-friendly
version lives at trnsci.dev/roadmap/.

What this phase means for trnsolver:
CG and GMRES are currently unpreconditioned. For chemistry and
engineering workloads, that's asymptotically fine but costs a lot
of iterations. Phase 3 adds Jacobi / SSOR preconditioners and
tunes them for NKI.

Done means:

• Jacobi preconditioner for CG lands (some work already in v0.2.x).
• Incomplete Cholesky preconditioner for CG (SPD systems).
• GMRES with restarts + preconditioning.
• Published benchmarks: iterations-to-convergence on canonical sparse Laplacians + chemistry-representative systems.
• NEFF cache reuse verified for preconditioner setup.

Coordination

• Label: phase-3-perf — matches the same label in every sub-project.
• Cross-project dependencies, if any, are called out in the "Done means"
  list above. Link any PRs / child issues here for tracking.

Close this issue when all "Done means" items are satisfied.

[scttfrdmn]

SSOR preconditioner landed in v0.8.0 (449657b), completing the remaining preconditioner item in this Phase 3 tracker.

ssor_preconditioner(A, omega=1.0) — applies M^{-1} r via:

1. Forward solve: (D + ω L) t = r
2. Scale: v = ω(2-ω) diag(A) ⊙ t
3. Backward solve: (D + ω L^T) z = v

At ω=1 (default) this is symmetric Gauss-Seidel. M_SSOR is SPD when A is SPD and ω ∈ (0, 2). Benchmark test_cg_ssor_precond added to benchmarks/bench_solver.py. BF16/FP16 inputs promoted to FP32 consistent with #19.

The remaining Phase 3 items — NEFF cache reuse in examples/benchmarks (#34) and sparse CG/GMRES on trnsparse matrices (#23) — are hardware-dependent or cross-project, so this tracker stays open.