Ridders' method

Ridders' method is a root-finding algorithm from numerical analysis, due to C. Ridders. It is built on the false position method, with an exponential factor applied to the function so that the estimate of the root improves quickly. Given two values on opposite sides of a root, the method evaluates the function at their midpoint, chooses the exponential parameter that makes the transformed function consistent with the average of the two end values, and then applies false position to the transformed points to get a new bracketing value. The root stays bracketed throughout. When the function is well behaved the formula converges quadratically, roughly doubling the number of correct significant digits at each step, but because the function is evaluated twice per step the order of convergence per evaluation is the square root of two. If the function is not well behaved the bracketing interval at least halves on each iteration, so convergence is guaranteed. The source describes it as simpler than Muller's method or Brent's method with similar performance.