Optimal Inequality Factor for Ehrlich-Aberth´s Method

The convergence condition for the simultaneous inclusion methods is w⁽⁰⁾ <; c_nd⁽⁰⁾, where w⁽⁰⁾ is the maximum Weierstrass factor W_k⁽⁰⁾, k ∈I_n, and d⁽⁰⁾ is the minimum distance between z₁⁽⁰⁾, z₂⁽⁰⁾, ...z_n⁽⁰⁾, the distinct approximations of the simple roots of the polynomial ζ₁, ζ₂, ...ζ_n. The i-factor (inequality-factor) is the positive function c_n = c(a,b, n) = 1/an+b. The article presents the optimum i- factor for the simultaneous inclusion Ehrlich-Aberth´s method.