Five iterative solvers race on the same 32×32 discrete Poisson problem (κ(A) ≈ 441): a +1 heat source near the NW corner and a −1 sink near the SE corner, with the matrix applied as a 5-point stencil and never stored. The two PCG variants use a HODLR approximation of A−1 — dense 64×64 diagonal leaves plus off-diagonal blocks truncated to rank 2 or rank 8 — loaded from the exact data exported by the experiments; Richardson uses the same rank-8 preconditioner with the optimal damping ω ≈ 0.7376 (undamped Richardson diverges at rank 8). Every run is precomputed to convergence at load, so the main slider scrubs the shared iteration history: drag it (or press Play) and all five panels plus the chart marker jump to frame k, with converged methods holding their final state. Background and derivations: report 14 — the hierarchical structure of the inverse.
| Method | iterations to 1e-6 | rel err at that iteration |
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Computed once at page load by running each solver to convergence (relative ℓ2 error vs the prefactored solution x*, capped at 2000 iterations).