445.747 Appproximation Theory

Study Guide 2000

Lecturer: Dr Shayne Waldron, room 410, phone 5877, e-mail waldron@math.auckland.ac.nz
Lecture Times: Monday, Wednesday, Friday 11:00 in in Room B10

This will be an introductory course in Approximation Theory, and does not require 445.740. Helpful background includes some linear algebra, real analysis and numerical analysis. The material complements that of 445.770, and is also of interest to analysts.

Assessment

There will be eight assignments, due on 26 July, 2 August, 16 August, 23 August, 20 September, 27 September, 11 October, 18 October, a one hour term test on 25 August (or there abouts), and a two hour final exam.

The grade will be made up of assignments (40%), term test (20%) and final exam (40%), or all on the final exam, which ever is best.

Syllabus

This includes classical topics: polynomial approximation (Weierstrass, Jackson, Bernstein, Korovkin theorems). univariate spline theory (B-splines, Schoenberg-Whitney theorem, blossoming), and some modern results: nonlinear approximation (wavelets, multiresolution analysis, subdivision), multivariate methods (radial basis functions, shift invariant spaces, Bernstein-Bezier forms).

Text books

The following relevant books are placed on reserve at the Science Library Desk.

Cheney, E. W., Introduction to Approximation Theory (1982)
Lorentz, G. G., Approximation of functions (1966)
Davis, P. J., Interpolation and Approximation (1963)
DeVore, R. A., Lorentz, G. G., Constructive Approximation (1993)
Feinerman, R. P., Newman, D. J., Polynomial approximation (1974)
Rivlin T. J., An introduction to the approximation of functions (1981)
Cheney, E. W., Light W., A course in Approximation Theory (1999)

For the first half the classic books of Cheney and Lorentz make good supplementary reading. I will cover selected topics from the recent book of Cheney and Light (Ward and Will) in second half.