README: correct benchmarks to use KLU as the honest baseline#3
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The prior numbers (a) compared against UMFPACK/dense, which fill or scale O(n^3) on the dense-row structure, overstating the advantage, and (b) included a benchmark bug that timed a dense n-by-n U*V formation as if it were re-KLU (the bogus ~785x/~650x figures). KLU's BTF+AMD isolates a few dense rows, so it is the honest sparse baseline: measured, Woodbury is ~1.7x faster on factor+solve and ~3x on the fixed-S reuse path at r=8 (the gap grows with the border width r). UMFPACK fills on the dense rows (~120x slower); dense is O(n^3). Co-Authored-By: Chris Rackauckas <accounts@chrisrackauckas.com> Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
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Corrects the README benchmarks per the analysis in our discussion:
S + U·Vwell and is the honest sparse comparison. Measured (n=5000, r=8): Woodbury 2.9 ms vs KLU 4.9 ms (~1.7×) on factor+solve, and 1.0 ms vs 3.0 ms (~3×) on the fixed-Sreuse path. The advantage grows with the border widthr.n×nU*Vintermediate every iteration — it was timing dense-matrix formation, not re-KLU.O(n³)(~280×).Docs-only. 🤖 Generated with Claude Code