Interpolation–Extrapolation/Regula Falsi Method/Method
Of False Position Consider the problem of locating the roots
of the polynomial f(x) = 0 with the trial points
x f x [ ] [ ] . 1 1 = 0 ( ) = −0 39672
and
x f x [ ] [ ] . . . 2 2 = 0 5 3 11808 ( ) =
These two trial points bound f(x) = 0. Interpolation–
extrapolation, also called the regula falsi method or the
method of false position, is simply a linear interpolation
between two bounding points to find the next trial point, x[3],
where f(x[3]) = 0 For subsequent iterations, two points are
retained, which keep f(x) = 0 bounded.
Develop the needed regula falsi equation and solve for
x[3]; also, provide the regula falsi equation in general form.
You cannot evaluate f(x[3]) as the constants ai in the polynomial are not provided.