Polynomials data fitting

Abstract

When we have a data table $ (x_0, y_0), (x_1, y_1), \ ldots (x_N, y_N) $ the question of how we can find a mathematical function that approximates this data is very common. One possibility is to look for a function that interpolates the data, that is, a function $ p $ that satisfies $ p (x_j) = y_j $ for $ j = 0,1, \ ldots, N $. Another possibility is to look for a function that fits the data in order to minimize errors between $ p (x_j) $ and $ y_j $ at all points. Polynomials are very simple functions and are therefore widely used for these approximations. In this project will be seen more generally interpolation methods, spline, uniform approximation and further studied the adjustment of least squares with weighted error and their relationship with orthogonal polynomials.