Locating and computing arbitrarily distributed zeros

The problem of locating and computing with certainty all the simple roots o f a twice continuously differentiable function f: [a, b] subset of R --> R is studied when some additional information on the distribution of the root s in the interval is available. The framework is the one proposed by [SIAM J. Sci. Comput., 17 (1996), pp. 1232-1248], where only the uniform case was examined. This paper settles some of the problems posed there and generali zes some of its results by considering an arbitrary distribution of the roo ts in [a, b]. The theoretical results are accompanied by simulations in a n umber of problems of various size.