Scope: This course is an introduction to a broad range of numerical methods for solving inverse type problems that arise in Science and Engineering. The goal is to provide a basic understanding of these numerical methods. This will help you choose and apply the appropriate numerical techniques for your problem and interpret the results.

Topics covered: Linear Regression, Discretization of continuous inverse problems, Rank Deficiency, Tikhonov Regularization, Iterative Methods, Fourier Techniques, Nonlinear Regression, Nonlinear Inverse Problems.


Prerequisites: Basic Linear Algebra. Some knowledge in MATLAB programming helps.

Textbook: "Parameter Estimation and Inverse Problems" by R.C. Aster, B. Borchers, and C.H. Thurber
Available from Amazon http://www.math.uconn.edu/~leykekhman/courses/MARN_5898/marn_5898.html

Syllabus

15 weeks.

This is intended schedule and most likey will be chahged during the semester.

Week 1: Ch 2. Linear regression.
Week 2: Ch 3. Discretization of continuous inverse problems.
Week 3: Ch 4. SVD decomposition and pseudoinverse.
Week 4: Ch 4. Rank deficiency and ill-conditioning.
Week 5: Ch 5. Tikhonov regularization.
Week 6: Ch 5. Tikhonov regularization (cond).
Week 7: Ch 6. Iterative methods.
Week 8: Ch 7. Additional regularization techniques.
Week 9: Ch 8. Fourier techniques.
Week 10: Ch 9. Nonlinear regression.
Week 11: Ch 10. Nonlinear inverse problems.
Week 12:
Week 13:
Week 14:
Week 15: