Instructor:Mohammad Motamed
General description
We will study several topics and concepts related to approximation and optimization from a numerical analysis perspective. We will utilize a combination of classical material and recent articles on the subject. We will also be working with Python for implementation. The following topics will be covered (time-permitting):
- Approximation of functions (70%)
- Polynomial interpolation
- Polynomial approximation (in uniform norm and 2-norm)
- Piecewise polynomial approximation (splines)
- Least squares and weighted least squares
- Trigonometric/Fourier-type approximation
- Nonlinear approximation
- Free-knot linear splines
- N-term approximation
- Artificial neural networks (ReLU networks and Fourier features)
- Numerical Optimization (20%)
- Convex optimization
- Stochastic optimization (stoch. gradient descent, Metropolis sampling, etc.)
- Numerical Integration and differentiation (10%)
Reading list
1) SM: Suli and Mayers. An Introduction to Numerical Analysis. 2) G: Gautschi. Numerical Analysis. 3) DB: Dahlquist and Bjorck. Numerical Mathods in Scientific Computing, Vol. I. 4) P: Lecture notes on probability To be completed ... Grading: Homework Assignments (see Homework Report Format) and in-class active participation
Homework Assignments
HW1: Homework no. 1 (posted: Sep 07, due: Sep 23 end of day) HW2: Homework no. 2 eval_spline.py (posted: Sep 27, due exended to Oct 23 end of day) HW3: Homework no. 3 (posted: Oct 28, due: Nov 20 end of day) HW4: Homework no. 4 (posted: Nov 28, due Dec 18 end of day) motamed@unm.edu
Last updated: Fall 2022