1 citations · 1 across the 9 of their papers we have counts for
9 papers
Rigid homotopies for sampling from algebraic varieties: a Waring structure complexity model
Abigail R. Jones, Kisun Lee, Jose Israel Rodriguez
Polynomial system solving has seen major progress in both theory and practice over the past decade. A landmark achievement was addressing Smale's 17th problem, establishing average…
Certifying Galois/monodromy Actions via Homotopy Graphs
Timothy Duff, Kisun Lee
We develop a certified numerical algorithm for computing Galois/monodromy groups of parametrized polynomial systems. Our approach employs certified homotopy path tracking to guaran…
Certified surface approximations using the interval Krawczyk test
Michael Burr, Jonathan D. Hauenstein, Kisun Lee
We propose an algorithm to construct a certified approximation of a surface by generalizing the Krawczyk test. The Krawczyk test is based on interval arithmetic, and confirms the e…
Asymptotic rank bounds: a numerical census
Kisun Lee
We systematically compute improved asymptotic rank bounds for tensors. Using numerical implicitization, we implement the geometric framework of Kaski and Michałek across all comput…
A priori bounds for certified Krawczyk homotopy tracking
Kisun Lee
We establish the first complexity analysis for Krawczyk-based certified homotopy tracking. It consists of explicit a priori stepsize bounds ensuring the success of the Krawczyk tes…
Certified algebraic curve projections by path tracking
Michael Burr, Michael Byrd, Kisun Lee
We present a certified algorithm that takes a smooth algebraic curve in and computes an isotopic approximation for a generic projection of the curve into $\mathbb{R}…
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…
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…
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…