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# Least squares approximation

Numerically, it is relatively simple to state the approximation problem for the least squares norm. This is the topic of this section.

## Linear least squares approximation

In the context of linear least squares approximation, it is always possible to reduce the problem to solving a system of linear equations, as the following example shows:

Consider the sine function f(x) = sin(x) in the interval from 0 to 1. We choose as approximants the polynomials of second degree: {a0 + a1x + a2x2}. To compute the values [a0, a1, a2] that minimize this problem, we first form a 3 × 3 matrix containing the pairwise dot products (the integral of the product of two functions) of the basic functions {1, x, x2} in the given interval. Because ...

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