ON ENCLOSING SIMPLE ROOTS OF NONLINEAR EQUATIONS

In this paper we present two efficient algorithms for enclosing a simp le root of the nonlinear equation f(x) = 0 in the interval [a, b]. The y improve recent methods of Alefeld and Potra by achieving higher effi ciency indices and avoiding the solution of a quadratic equation per i teration. The efficiency indices of our methods are 1.5537 ... and 1.6 18... , respectively. We show that our second method is an optimal alg orithm in some sense. Our numerical experiments show that the two meth ods of the present paper compare well with the above methods of Alefel d and Potra as well as efficient solvers of Dekker, Brent, and Le. The second method in this paper has the best behavior of all, especially when the termination tolerance is small.