Numerical Approximation Theory

Department: 
MATH
Course Number: 
6645
Hours - Lecture: 
3
Hours - Lab: 
0
Hours - Recitation: 
0
Hours - Total Credit: 
3
Typical Scheduling: 
Every odd spring

Theoretical and computational aspects of polynomial, rational, trigonometric, spline and wavelet approximation.

Prerequisites: 

MATH 4317 and MATH 4640

Course Text: 

No text

Topic Outline: 
  • Polynomial Approximations - Chebyshev and least squares approximation, orthogonal polynomials, B-splines, Bezier curves, interpolation, linear methods of approximation
  • Trigonometric Polynomial Approximation - Fourier series and the FFT, orthogonal polynomials on the unit circle
  • Wavelet Approximation - Bernstein and Jackson Theorems, Strang-Fix condition, fast decomposition reconstruction, multiwavelet approximation
  • Error and Mesh Generation - Triangulation of surfaces, mesh and order selection, accuracy and regularity
  • Multivariate Problems
  • Applications - Graphics, signal processing, integration, and data compression