Quadratic Fit

Quadratic fit is a derivative-free method designed for univariate functions.

Algorithm: Quadratic Fit

$$ 0. Start with an initial inverval $$ and a point $$ in the interval. Let $$ be a termination tolerance.
$$ 1. If $$, stop and return $$ as the minima.
$$ 2. Compute $$.
$$ If $$, go to Step 3.
$$ If $$, go to Step 4.
$$ If $$, go to Step 5.
$$ 3. If $$, then $$ and go to Step 4; else $$ and go to Step 5.
$$ 4. If $$, then $$; otherwise $$ and $$. Go to Step 1.
$$ 5. If $$, then $$; otherwise $$ and $$. Go to Step 1.

$$ is computed as:

$$

where $$, $$.