Interval methods for root-finding of nonlinear equations of one variable

Interval analysis has proven successful for finding a root ξ of a nonlinear equation f(x)=0 in the interval [a,b]. The classical version of interval Newton's method and more three new (supposed) interval methods has been tested on a series of examples. The Regula Falsi-Newton hybrid interval method and Halley's (two versions) interval method are competitive when compared with the interval Newton's method (used version). The numerical results empirically show that all methods give us verified computations (self-validating), ensuring that the exact value is certain to belong to the intervals computed.