What is false position method?

The false position method is a numerical iterative method used to approximate a root of a given function. It is also known as the regula falsi method, meaning "false rule" in Latin.

In this method, two initial points are chosen, one lying on either side of the root. The function is evaluated at both points, and a line is drawn connecting these two points. The root is then estimated as the point where this line intersects the x-axis.

Next, the function is evaluated at the estimated root point. If the result has the same sign as the function value at one of the initial points, that initial point is discarded and the estimated root becomes the new initial point. If the result has the same sign as the function value at the other initial point, that initial point is discarded and the estimated root becomes the new initial point.

This process continues until the desired level of accuracy is achieved. The false position method is a reliable and efficient method when the function is continuous and has a single root within the given interval. However, if the function has multiple roots or the interval is not well-defined, the method may not work well, and other numerical methods may be more appropriate.