On the condition of algebraic equations

Summary Given an algebraic equation, in which the polynomial in question is expressed in terms of any set of basis polynomials, we study the sensitivity of the roots with respect to small perturbations in the coefficients of the equation. The degree of sensitivity of each root is measured by an appropriate condition number. We analyze this condition number first in the case where the basis polynomials are the powers, and then, in less detail, in the case where the basis is a set of orthogonal polynomials. Several examples are treated, allowing for a comparative study.Work performed in part at the U.S.A.F. Aerospace Research Laboratories under contract F33615-71-C-1463 with Technology Incorporated.