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Authors: Rokne, Jon
Keywords: Computer Science
Issue Date: 1-Jan-1976
Abstract: A central problem in interval analysis is the computation of the range of values of an interval polynomial over an interval. This problem has been treated by Dussel and Schmitt [1] and, disregarding the computational cost of their algorithm, solved in a satisfactory manner. In this paper we will discuss two algorithms by Rivlin [4] (see also Cargo and Shiska [2]) where the accuracy of the bounds depend on the amount of work one is willing to do. The first algorithm is based upon the expression of a polynomial in Bernstein polynomials. This algorithm as given by Rivlin [4] is valid for an estimate over the interval [0,1]. We will generalize the algorithm to an arbitrary finite interval and we will show that it is an appropriate algorithm if the width of the interval is not too large. The second algorithm is based upon the mean value theorem. As stated by Rivlin [4] it is valid for the interval [0,1]. We will generalize the algorithm so that it is valid for any finite interval. The algorithms are then generalized to interval arithmetic versions. Finally we compare the algorithms numerically on several polynomials.
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