# Approximation Theory

Engineering, finance, science, and many areas of mathematics itself make use of quantities that are too complicated, too difficult, and even too abstract to work with directly. A major goal of approximation theory is to discover and analyze simple, easy to work with, concrete quantities that can do a good, efficient job in their place - for example, splines to fit messy curves, wavelets to analyze noisy signals and to compress large images, and radial basis functions to fit scattered data and serve as the ``approximation engine'' of neural networks.

Areas of faculty interest include approximations by orthogonal polynomials, radial basis functions, and wavelets; futher topics of interest include scattered data surface fitting, rates of approximation, constrained approximation, polynomial inequalities, orthogonal polynomials, wavelets, splines, non-linear approximation. There is significant overlapping interests with the groups in partial differential equations and numerical analysis.