Two Algorithms for Root Finding in
نویسندگان
چکیده
We present two algorithms for computing the root, or equivalently the xed point, of a function in exact real arithmetic. The rst algorithm uses the iteration of the expression tree representing the function in real arithmetic based on linear fractional transformations and exact oating point. The second and more general algorithm is based on a trisection of intervals and can be compared with the well-known bisection method in numerical analysis. It can be applied to any representation for exact real numbers; here it is described for the sign binary system in ?1; 1] which is equivalent to the exact oating point with linear fractional transformations.
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