A note on the growth factor in Gaussian elimination for accretive-dissipative matrices |
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Authors: | Minghua Lin |
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Affiliation: | 1. Applied Mathematics Department, University of Waterloo, Waterloo, ON, N2L 3G1, Canada
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Abstract: | This short note proves that if \(A\) is accretive-dissipative, then the growth factor for such \(A\) in Gaussian elimination is less than \(4\) . If \(A\) is a Higham matrix, i.e., the accretive-dissipative matrix \(A\) is complex symmetric, then the growth factor is less than \(2\sqrt{2}\) . The result obtained improves those of George et al. in Numer. Linear Algebra Appl. 9, 107–114 (2002)] and is one step closer to the final solution of Higham’s conjecture. |
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