Least Squares Approximation

In many applications we want to find an approximation for a function, for example for differential equations. Example problem: We want to understand how a calculator or computer can evaluate sinx for a given value x. The processor can essentially only perform addition, multiplication, division. Therefore we can try to approximate the function with a polynomial. We use the notation Pn for polynomials of degree≤ n: Pn = { c0 + c1x+ · · ·+ cnx | c j ∈ R }