Abstract
In this paper gradient flows on unitary matrices are studied that maximize the real part of the C-numerical range of an arbitrary complex n×n-matrix A. The geometry of the C-numerical range can be quite complicated and is only partially understood. A numerical discretization scheme of the gradient flow is presented that converges to the set of critical points of the cost function. Special emphasis is taken on a situation arising in NMR spectroscopy where the matrices C,A are nilpotent and the C-numerical range is a circular disk in the complex plane around the origin.
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Helmke, U., Hüper, K., Moore, J. et al. Gradient Flows Computing the C-numerical Range with Applications in NMR Spectroscopy. Journal of Global Optimization 23, 283–308 (2002). https://doi.org/10.1023/A:1016582714251
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DOI: https://doi.org/10.1023/A:1016582714251