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  "body": "\n## Summary\n\nFunction approximation is the task of choosing, from a fixed class of simple functions, one that is close to a given target function.\nCloseness is measured by a [[norm|0V2WP9B1MF]], for instance the largest pointwise difference or a mean square difference.\nThe task appears in numerical analysis, in signal processing and in machine learning, where the target is often known only through samples.\n\n## Explanations\n\n### L1 human\n\nImagine a complicated curve that you want to replace by something easy to store and evaluate.\nYou choose a family of easy curves, such as polynomials of degree $2$, and pick one whose graph stays near the target.\nFor instance, on $[0, 1]$ the polynomial $1 + x + x^2/2$ stays within $0.22$ of $e^x$.\nHow good such a replacement can be depends on the family you allow and on how you measure the gap.\n",
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