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• W2048562977 abstract "We describe, for the first time, a completely rigorous homotopy (path-following) algorithm (in the Turing machine model) to find approximate zeros of systems of polynomial equations. If the coordinates of the input systems and the initial zero are rational our algorithm involves only rational computations, and if the homotopy is well posed an approximate zero with integer coordinates of the target system is obtained. The total bit complexity is linear in the length of the path in the condition metric, and polynomial in the logarithm of the maximum of the condition number along the path, and in the size of the input." @default.
• W2048562977 created "2016-06-24" @default.
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• W2048562977 date "2013-02-01" @default.
• W2048562977 modified "2023-10-02" @default.
• W2048562977 title "Robust Certified Numerical Homotopy Tracking" @default.
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• W2048562977 doi "https://doi.org/10.1007/s10208-013-9143-2" @default.
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