General Superiority for the Real Closest Normal Matrix Problem

Determine whether Guglielmi and Scalone’s algorithm is generally superior to the proposed Riemannian optimization method for computing closer real normal matrices.

Background

On the tested Real Closest Normal Matrix Problem instances, Guglielmi and Scalone’s algorithm obtains lower residuals more often, whereas the proposed method is faster and produces matrices satisfying normality more accurately under the stopping criteria. Because these finite experiments yield no definitive general comparison, the relative global optimization quality of the two methods remains unresolved.

References

While Guglielmi and Scalone's method obtained lower residuals than our approach on $6/9$ of the tested instances on the Real CNP, it is inconclusive to say whether their method is generally superior to ours at determining closer real normal matrices.

— The Normal Procrustes Problem: A Riemannian Optimization Approach  (2608.19513 - Bierly, 20 Aug 2026) in Section 8.2, subsection “Comparison with Guglielmi and Scalone’s Algorithm over the Real CNP”