Approximation Theory

Description

Approximation theory lies at the interface of many specialties. As such its study involves an interesting mix of pure and applied mathematics. At the pure end it is the study of the properties certain spaces of functions. Examples being polynomials, splines radial basis functions and Bézier
surfaces. At the applied end it is the construction of algorithms to enable efficient use of these spaces of functions in practical problems.

Recent applications of Approximation Theory here at UC include fitting surfaces to noisy point clouds, applied to the custom manufacture of artificial limbs, and fitting geophysical data sets such as gold grade measurements from drill holes in mines.

The first part of this course will concentrate on the fundamentals of approximation of functions of one variable. Central topics will be approximation by algebraic and trigonometric polynomials, and the existence, characterisation and uniqueness of best approximations from finite dimensional normed linear spaces.

In the latter part of the course we will develop some more recent topic. The exact topic will be chosen by the class. Examples of possible topics are radial basis functions, the use of Bézier surfaces in modeling, and penalized least squares and L1 methods for modeling noisy data.


For a full list of Honours courses, please refer to the School of Mathematics and Statistics Honours Booklet Mathematics and Statistics Honours Booklet