MARN 5898:
Parameter Estimation and Inverse Methods in Environmental Sciences
Spring 2010

Friday, 10:00 - 12:00pm, MAR 122
Instructors: Dmitriy Leykekhman, James O'Donnell

General information

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


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: