Investigate anomalous runtime spike at matrix size 192 in Maple experiments

Investigate the cause of the extremely large computation time observed for matrix size 192 when computing the JordanForm and FrobeniusForm in Maple 2021 for the test matrices whose characteristic polynomial has two irreducible factors of equal degree (structure {4,0,0,1} for f1 and {2} for f2), as described in Section 5.4; ascertain why the runtime spikes at size 192 compared to neighboring sizes under the same experimental setup.

Background

The paper proposes an exact algorithm for computing the structure of Jordan blocks via Jordan-Krylov bases and compares its performance against Maple’s LinearAlgebra routines (JordanForm and FrobeniusForm) across several experimental settings. In Section 5.4, the authors consider matrices whose characteristic polynomial has two irreducible factors of equal degree; the structure associated to f1 is {4,0,0,1} and to f2 is {2}.

In the Maple comparison for this setting, a notable anomaly was observed: the computation time for matrix size 192 was extremely large relative to other sizes (see the Maple table in that subsection). The authors explicitly state that the reason for this outlier is unknown and call for further investigation into its cause.