A new class of interval methods with higher order of convergence (Q1122314)

An interval iteration procedure for the inclusion of simple roots of nonlinear equations \(f(x)=0\) is described., where f is twice continuouly differentiable. Each step of the iteration procedure requires several function values and one interval evaluation of the second derivative. It is shown that if \(s\geq 5\) function values are used, then the order of convergence grows exponentially with s as \(((1+\sqrt{5})/2)^{s+1}\). Numerical experiments are reported.