Summary
We use numerical optimization techniques to search for matrices with bounded coefficients that have orthogonal columns of large euclidean norm. This leads to lower bounds for the maximum relative growth of the coefficients arising in a Gaussian matrix decomposition into triangular factors. For the complete pivoting strategy, Wilkinson has conjectured in 1963 that such relative growth should not exceedn, the order of the matrix.
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References
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Puschmann, H., Cortés, J. The coordinex problem and its relation to the conjecture of Wilkinson. Numer. Math. 42, 291–297 (1983). https://doi.org/10.1007/BF01389574
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DOI: https://doi.org/10.1007/BF01389574