3 papers
math.AG2022
Sparse trace tests
Taylor Brysiewicz, Michael Burr
We establish how the coefficients of a sparse polynomial system influence the sum (or the trace) of its zeros. As an application, we develop numerical tests for verifying whether a…
math.NA2020
Inflation of poorly conditioned zeros of systems of analytic functions
Michael Burr, Anton Leykin
Given a system of analytic functions and an approximate zero, we introduce inflation to transform this system into one with a regular quadratic zero. This leads to a method for iso…
cs.SC2019
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…