Measured exponents are not the predicted ones

Time Cholesky, LU, QR, eigh and SVD across n = 128 … 768, fit log t against log n, and the slope is the measured exponent.

It does not come out at 3.0. Fitted slopes land near 2.2–2.9, and the measured SVD/Cholesky ratio lands well under the 39× the table predicts.

That is not a failure of the theory. Parallelism and cache reuse both improve as n grows, so the machine gets faster at the same work and the curve flattens. The effect shrinks with larger n, so the slope creeps upward.

What survives is the ratio between methods at fixed n. It cancels the machine out, because both methods gain from the same hardware. Predict with ratios, not exponents.