Determine the cause of the superlinear empirical scaling of the dense eigensolver

Determine whether memory pressure causes the observed scaling of LAPACK’s dggev generalized eigensystem solver to be closer to O(L^7) than its theoretical O(L^6) scaling as the highest spherical-harmonic mode L increases.

Background

The approximate Killing vector spin calculation discretizes a generalized eigenvalue problem whose matrix dimension scales as O(L2), where L is the highest spherical-harmonic mode used to represent the apparent horizon. A dense LAPACK dggev solve therefore has theoretical time complexity O(L6).

For the numerical experiments reported in the paper, the measured scaling is closer to O(L7). The authors suggest that memory pressure may explain the discrepancy but explicitly state that this explanation has not been rigorously verified, leaving the cause of the observed scaling unresolved.

References

In our simulations, we have found the scaling to be closer to $\mathcal{O}(L7)$, as shown in Figs. (\ref{fig:HPC_all_in_one}) and (\ref{fig:PC_all_in_one}). We suspect that the slightly worse scaling may be due to memory pressure since the matrix has $\mathcal{O}(L4)$ elements, although we have not rigorously verified this.

— Finding black hole spins efficiently during a numerical binary evolution  (2608.12211 - Chaudhary et al., 12 Aug 2026) in Section 2, “Current AKV algorithm”