inverse quadratic interpolation

Concept

for every iteration
$u=f(b)/f(c)$, $v=f(b)/f(a)$, $w=f(a)/f(c)$

$$p=v(w(u-w)(c-b-(1-u)(b-a)))$$ $$q=(w-1)(u-1)(v-1)$$

then
$c=a$, $a=b$ and $b=b+p$