Curve Fitting Using Calculus in Normed Spaces

Abstract: Curve fitting is used in a variety of fields, especially in physics, mathematics and economics. The method is often used to smooth noisy data and for doing path planning. In this bachelor thesis calculus of variations will be used to derive a formula for finding an optimal curve to fit a set of data points. We evaluate a cost function (defined on the set of all curves f on the interval [ a; b]) given by F(f) = R b a (f00(x))2dx + P n i =1(f(xi)