Abstract
When solving polynomial systems with homotopy continuation, the fundamental numerical linear algebra computations become inaccurate when two paths are in close proximity. The current best defense against this ill-conditioning is the use of adaptive precision. While sufficiently high precision indeed overcomes any such loss of accuracy, high precision can be very expensive. In this article, we describe a simple heuristic rooted in monodromy that can be used to avoid the use of high precision.
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Bates, D.J., Niemerg, M. Using Monodromy to Avoid High Precision in Homotopy Continuation. Math.Comput.Sci. 8, 253–262 (2014). https://doi.org/10.1007/s11786-014-0190-0
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DOI: https://doi.org/10.1007/s11786-014-0190-0