# L1, L2, and LP Norms  One point missing (or not stressed out enough) is that the higher $p$ is, the more important is the contribution of large errors (e.g points far from the values to evaluate). On the contrary, the lower $p$ is the higher the contribution of the small errors. So a large $p$ will favour estimations that have small maximal errors whereas small $p$ will favour estimations that stay close to the function overall allowing large spikes in places. This is particularly visible comparing $L_1$ and $L_{\infty}$. $L_{\infty}$ will be high for a perfect match except for a single point being far from the function to estimate, when $L_0$ will be $0$. On the opposite, $L_{\infty}$ will be small (=epsilon) for an estimate e(x) = f(x) + epsilon whereas $L_1$ would be epsilon*(b-a) where [a,b] is the integration domain (so large error). --- Date: 20230113 Links to: Tags: #review References: * [The Lp Norm for Vectors and Functions - YouTube](https://www.youtube.com/watch?v=NKuLYRui-NU)