Least squares approximation

Summary

Least squares approximation replaces a function by the element of a given finite-dimensional family that is closest in a mean square sense. It is the best approximation in an inner product space, so it is the orthogonal projection onto the family. Unlike the uniform best approximation, it is found by solving a linear system, and an orthogonal basis makes it explicit. It is the function version of the least squares method for linear systems.