In connection with a CompSciSE question about largest eigenvalue of PSD matrics, I'd like to know which (nonzero) quadratic polynomial $f(x)$ minimizes the ratio:
$\frac{\max_{0 \le x \le 0.8} |f(x)|}{|f(1)|}$
[The goal is making a robust improvement on the simple power method's rate of convergence without having to code a Lanczos-like algorithm.]
Of course the method of solution is of greater interest than the specific polynomial. I see that the answer is not unique, insofar as any nonzero multiple of $f(x)$ gives the same ratio. So perhaps one wants to restrict attention to the cases $f(1) = 1$.