## Min-Max Elementwise Backward Error for Roots of Polynomials and a Corresponding Backward Stable Root Finder KU Leuven

A new measure called min-max elementwise backward error is introducedfor approximate roots of scalar polynomials $p(z)$.Compared with the elementwise relative backward error, this new measure allows forlarger relative perturbations on the coefficients of $p(z)$ that do not participate muchin the overall backward error.By how much these coefficients can be perturbed is determinedvia an associated max-times polynomial and its tropical roots.An ...