Summary: Algorithm 748: Enclosing Zeros
of Continuous Functions
G. E. ALEFELD
F. A. POTRA
University of lowa
Two effiden! algorithms for enclosing a zero of a continuous function are presented. They are
similar to the recent methods. but together with quadratic interpolation they make essential use
of inverse cubic interpolation 38.weIl Since asymptotica1ly the inverse cubic interpo~ation is
always choSen by the algorithms. they achieve higher-efficiency indices: 1.6529... for the first
algorithm. and 1.6686... for the second one. It i8 proved that the second algorithm is optimal in
a certain family. Numerica1 experiments show that the two n~w methods compare well with
recent methods. as weil 88 with the efficient solvers of Dekker. Bren~ Bus and Dekker. arid Le.
The second method from the present artic1e has the best. behavior of all 12 methods especially
when the termination tolerance is sma1l .
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Gategories and Subject Descriptors: G.1.0 [Numerical Analysis]: General-numerical algo-