Spring 1999, MW 3:30-4:45
This will be an introductory graduate level course on approximation theory. We will focus mainly on Linfinity and L2 approximation, with an introduction to L1 approximation. The last third of the course will be an introduction to the theory of splines and their approximation properties. Topics include normed linear spaces, best approximations, polynomial interpolation and divided differences, osculatory interpolation, Linfinity approximation, the Remes exchange algorithm, rational approximation, L2 approximation, orthogonal polynomials, trigonometric pproximation to periodic functions, piecewise polynomials and splines, B-splines, convergence properties of spline approximations, smoothing splines.