1 citations · 1 across the 7 of their papers we have counts for
9 papers
Two-step Newton's method for deflation-one singular zeros of analytic systems
Kisun Lee, Nan Li, Lihong Zhi
We propose a two-step Newton's method for refining an approximation of a singular zero whose deflation process terminates after one step, also known as a deflation-one singularity.…
Isolating clusters of zeros of analytic systems using arbitrary-degree inflation
Michael Burr, Kisun Lee, Anton Leykin
Given a system of analytic functions and an approximation to a cluster of zeros, we wish to construct two regions containing the cluster and no other zeros of the system. The small…
Homotopy techniques for analytic combinatorics in several variables
Kisun Lee, Stephen Melczer, Josip Smolčić
We combine tools from homotopy continuation solvers with the methods of analytic combinatorics in several variables to give the first practical algorithm and implementation for the…
The NumericalCertification package in Macaulay2
Kisun Lee
The package \texttt{NumericalCertification} implements methods for certifying numerical approximations of solutions for a given system of polynomial equations. For certifying regul…
On the polyhedral homotopy method for solving generalized Nash equilibrium problems of polynomials
Kisun Lee, Xindong Tang
The generalized Nash equilibrium problem (GNEP) is a kind of game to find strategies for a group of players such that each player's objective function is optimized. Solutions for G…
Implementing real polyhedral homotopy
Kisun Lee, Julia Lindberg, Jose Israel Rodriguez
We implement a real polyhedral homotopy method using three functions. The first function provides a certificate that our real polyhedral homotopy is applicable to a given system; t…
Typical ranks in symmetric matrix completion
Daniel Irving Bernstein, Grigoriy Blekherman, Kisun Lee
We study the problem of low-rank matrix completion for symmetric matrices. The minimum rank of a completion of a generic partially specified symmetric matrix depends only on the lo…
Effective certification of approximate solutions to systems of equations involving analytic functions
Michael Burr, Kisun Lee, Anton Leykin
We develop algorithms for certifying an approximation to a nonsingular solution of a square system of equations built from univariate analytic functions. These algorithms are based…
Solving polynomial systems via homotopy continuation and monodromy
Timothy Duff, Cvetelina Hill, Anders Jensen +3
We study methods for finding the solution set of a generic system in a family of polynomial systems with parametric coefficients. We present a framework for describing monodromy ba…