Accuracy of the kernel approximation of functions ↩

aliases: []
shorthands: {}
created: 2022-04-25 14:03:03
modified: 2022-04-25 14:17:29

Where stands for residual.

Derivation

Let's start from the kernel approximation:

And use the Taylor expansion of around .

Here we used the normalization condition of the smoothing function and the fact that is odd if is even, so its integral vanishes. The residual will depend on because of the compact condition .