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# Chapter 2. Interpolation and Approximation

Approximation theory states how to find the best approximation to a given function by another function from some predetermined class and how good this approximation is. In this chapter, we are going to explore this field through two settings: interpolation and least squares approximation.

# Motivation

Consider a meteorological experiment that measures the temperature of a set of buoys located on a rectangular grid at sea. We can emulate such an experiment by indicating the longitude and latitude of the buoys on a grid of 16 × 16 locations, and random temperatures on them between say 36ºF and 46ºF:

```In [1]: import numpy as np, matplotlib.pyplot as plt, \
...: matplotlib.cm as cm; \
...: from mpl_toolkits.basemap ...```

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