Two Efficient Algorithms with Guaranteed Convergence for Finding a Zero of a Function

Two algorithms are presented for finding a zero of a real continuous function defined on a given interval. The methods used are mixtures of linear interpolation, rational interpolation, and bisectmn. The asymptotic behavior of these algorithms is completely satisfactory. The munber of function evaluations needed to find a zero of a function is bounded by four or five times the number needed by bisection and is usually considerably smaller.