So, I need to find the second-degree polynomial that is the best approximation for $f(x) = cos(x)$ in $L^2_w[a, b]$, where $w(x) = e^{-x}$, $a=0$, $b=\infty$.
"Best approximation" for f is a function $\hat{\varphi} \in \Phi$ such that:
$||f - \hat{\varphi}|| \le ||f - \varphi||,\; \forall \varphi \in \Phi$
I have several methods available:
- Lagrange interpolation
- Hermite interpolation
Which would be the most appropriate?