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cs.SC2024
Effective alpha theory certification using interval arithmetic: alpha theory over regions
Kisun Lee
We reexamine Smale's alpha theory as a way to certify a numerical solution to an analytic system. For a given point and a system, Smale's alpha theory determines whether Newton's m…
math.CO2024
The Tropical Variety of Symmetric Rank 2 Matrices
May Cai, Kisun Lee, Josephine Yu
We study the tropicalization of the variety of symmetric rank two matrices. Analogously to the result of Markwig and Yu for general tropical rank two matrices, we show that it has…
math.NA2024★ 1 cited
Certified homotopy tracking using the Krawczyk method
Timothy Duff, Kisun Lee
We revisit the problem of certifying the correctness of approximate solution paths computed by numerical homotopy continuation methods. We propose a conceptually simple approach ba…