Die vollautomatische Berechnung einer einfachen Nullstelle von F(t)=0 einschließlich einer Fehlerabschätzung

Abstract

An always converging method is given for the solution of the equation F(t)=0. If F(t) has only one root Z in the basic interval [a, b] then optimal bounds for Z can be evaluated. The algorithm given uses the method of interval-halfing several times. It is essential for the construction of the bounds for Z that the value of the function F(t) be computed with the aid of an errorbound-arithmetic. © 1967 Springer-Verlag.