The false position method is a root-finding algorithm that uses linear interpolation to estimate the root of a function. It improves upon the bisection method by using the function values at the endpoints of the interval rather than just their signs. The method chooses the intercept of the secant line through the two endpoints as the next approximation of the root, and continues iteratively narrowing the interval until the root is found.

1. REGULAFALSI METHODFalse Position Method

2. False-Position MethodIt seems that the simplest methods often converge the slowest. This certainly seems the case here. The bisection method does not use values of . Only their sign. However, the values could be exploited. One way to use values of is to bias the search according to value of : use a weighted average

3. False-Position MethodChoose as the intercept of the secant line through and . Pick , theinterceptthen

4. False-Position Method

5. False-Position Method is first approximation to As in bisection, if or there must be a root Suppose , then SOURCE: http://www.ece.uwaterloo.ca/~dwharder/NumericalAnalysis/10RootFinding/falseposition/examples.html