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Orthogonal growth problem for GEPP

Determine the maximum possible growth factor under Gaussian elimination with partial pivoting (GEPP) when the input matrix is orthogonal. Characterize the worst-case GEPP growth over A ∈ SO(n).

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Background

The growth problem seeks worst-case bounds for Gaussian elimination. Restricting to orthogonal matrices forms a natural subclass relevant to Hadamard matrices. While GEPP is widely used, the worst-case growth for orthogonal inputs has not been settled.

The paper mentions recent exploration of this problem, underscoring that it remains unresolved.

References

For instance, the orthogonal growth problem remains open in GEPP even, which was recently explored in .

— Complete pivoting growth of butterfly matrices and butterfly Hadamard matrices (2410.06477 - Peca-Medlin, 9 Oct 2024) in Section 1 (Introduction)