Bounds on Distance to Variety in Terms of Coefficients of Bivariate Polynomials

This work offers theoretical guarantees for numerical algebraic geometry, but the results are incremental and specialized to bivariate polynomials.

The paper derives bounds on the distance from a point to a variety defined by a bivariate polynomial, expressed in terms of the Taylor coefficients at that point. The results provide quantitative estimates for how close a point can be to the zero set of a polynomial.