Least Square Problems

Almost all kinds of approximation are based on the principle that a complicated function is represented by a simpler function that is easy to evaluate. This simpler function has a certain number of parameters that are determined such that the approximation error is small in some sense. The finite element method for differential equations is based on this idea. In order to understand the principles, we discuss in this chapter the simpler problem of approximating a given function without any differential equations involved.