Author:

Keywords:

backward error, roots of polynomials, tropical backward error, elementwise mixed backward error, tropical roots, Science & Technology, Physical Sciences, Mathematics, Applied, Mathematics, Backward error, Roots of polynomials, Tropical backward error, Element-wise mixed backward error, Tropical roots, EIGENVALUES, 0102 Applied Mathematics, 0103 Numerical and Computational Mathematics, 0802 Computation Theory and Mathematics, Numerical & Computational Mathematics, 4901 Applied mathematics, 4903 Numerical and computational mathematics

Abstract:

We analyze different measures for the backward error of a set of numerical approximations for the roots of a polynomial. We focus mainly on the element-wise mixed backward error introduced by Mastronardi and Van Dooren, and the tropical backward error introduced by Tisseur and Van Barel. We show that these measures are equivalent under suitable assumptions. We also show relations between these measures and the classical element-wise and norm-wise backward error measures.