Algorithm 748

Algorithm 748; enclosing zeros of continuous functions. The authors present two new modifications of their previously published algorithms for enclosing a zero of a continuous function $f(x)$. The modifications involve the use of inverse cubic interpolation rather than quadratic interpolation. The paper also discusses their earlier algorithms, and compares these algorithms with other standard routines. Although the new algorithms are marginally more economical in terms of function evaluations, it is striking how well Brent’s method compares in practice, 25 years after its introduction.

This software is also peer reviewed by journal TOMS.