ALGORITHM 748 - ENCLOSING ZEROS OF CONTINUOUS-FUNCTIONS

Two efficient algorithms for enclosing a zero of a continuous function are presented. They are similar to the recent methods, but together w ith quadratic interpolation they make essential use of inverse cubic i nterpolation as well. Since asymptotically the inverse cubic interpola tion is always chosen by the algorithms, they achieve higher-efficienc y indices: 1.6529... for the first algorithm, and 1.6686... for the se cond one. It is proved that the second algorithm is optimal in a certa in family. Numerical experiments show that the two new methods compare well with recent methods, as well as with the efficient solvers of De kker, Brent, Bus and Dekker, and Le. The second method from the presen t article has the best behavior of all 12 methods especially when the termination tolerance is small.