Implements the Regula Falsi or False position method for root-finding (approximating a zero of a univariate real function). It is a modified Secant method.

The Regula Falsi method is included for completeness, for testing purposes, for educational purposes, for comparison to other algorithms, etc. It is however not intended to be used for actual problems, as one of the bounds often remains fixed, resulting in very slow convergence. Instead, one of the well-known modified Regula Falsi algorithms can be used (Illinois or Pegasus). These two algorithms solve the fundamental issues of the original Regula Falsi algorithm, and greatly out-performs it for most, if not all, (practical) functions.

Unlike the Secant method, the Regula Falsi guarantees convergence, by maintaining a bracketed solution. Note however, that due to the finite/limited precision of Java's double type, which is used in this implementation, the algorithm may get stuck in a situation where it no longer makes any progress. Such cases are detected and result in a ConvergenceException exception being thrown. In other words, the algorithm theoretically guarantees convergence, but the implementation does not.

The Regula Falsi method assumes that the function is continuous, but not necessarily smooth.

Implementation based on the following article: M. Dowell and P. Jarratt, A modified regula falsi method for computing the root of an equation, BIT Numerical Mathematics, volume 11, number 2, pages 168-174, Springer, 1971.