Abstract:

One of the most commonly used interpolation methods is based on the use of cubic splines due to their ease of handling (these are functions with a second continuous derivative and that, in pieces, are given by cubic polynomials) and its good geometric properties (they are the curves with the smallest "curvature" that happen through a given points). Splines can also be used to find the best least-squares approximation for a set of given points. In this paper we present a virtual laboratory of Matlab that allows to study graphically the least squares approximation through cubic splines and their properties. It is possible to work from a set of points of the given plane or from a curve defined by a function. In this case, in addition to the graphical representation of the given points, the exact curve and the least squares approximation, the graph of the error can also be obtained. The application can show the polynomial approximation by least squares allowing to compare both methods. Simplicity of handling, speed of calculation, interactivity and multiple graphical options can help students to better understand the concept of quadratic least approximation by splines, their properties and comparison with other methods.

Keywords:

Splines, interpolation, least squares, virtual laboratory, Matlab, graphical interface, active methodologies.