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FALSE POSITION
The convergence rate of the bisection method could possibly be improved by using a different solution estimate.
This method calculates the new solution estimate as the x-intercept of the line segment joining the endpoints of the function on the current bracketing interval. Essentially, the root is being approximated by replacing the actual function by a line segment on the bracketing interval and then using the classical double false position formula on that line segment.
The first two iterations of the false position method. The red curve shows the function f and the blue lines are the secants.
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