Lectures

This page will be updated after class and is meant to serve as a historical record of what has been covered. Also, sample codes presented during lecture will be provided here. Reading assignments are from Aster unless otherwise noted.

Topic Material Examples
Week 1 Intro and Basic Concepts Ch 1, Appendix A
08/29 Intro to Inverse Methods 1.1-1.3, Tarantola (2006)
08/31 Ill-posed and Ill-conditioned 1.4 - 1.6, A7, A8
Week 2 Least Squares Regression Ch 2, B
09/05 Intro to Least Squares 2.1 - 2.4 g.txt, d.txt, race_inclass.m
09/07 Errors, covariance, Student's t-test Appendix B
Week 3 Least Squares and SVD Ch 2, Appendix A, B
09/12 Multiple Least Squares and Model Selection Ch. 2 crime_class.m, crime_data.txt, linear_vs_cubic.m, linear_vs_cubic.txt
09/14 Singular Value Decomposition Ch 3
Week 4 SVD and Regularization Ch 3
09/19 Ill-posed problems, SVD spectrum, Resolution 3.2, 3.4 tomo_class.m
09/21 TSVD 3.3 - 3.5 ex_3_3.m
Week 5 Tikhonov Regularization Ch 4
09/26 Tikhonov, L-curve 4.1 - 4.4
09/28 MAP, aggregation, cross validation Trace gas inversion articles, 4.8
Week 6 Midterm Ch 1 - 4
10/03 Generalized CV, midterm review 4.1 - 4.4
10/05 Midterm
Week 7 Iterative Methods Ch 6
10/10 Steepest Descent sd_ex.m, sd.m.
10/12 Midterm review, Conjugate Gradient 6.3, Painless CG
Week 8 Iterative and Nonlinear Methods Ch 6, 9
10/17 CG, CGLS, Newton's Method cgls.m, newton.m.
10/19 Gauss-Newton, Levenberg-Marquardt gn_start.m.
Week 8 Nonlinear Problems Ch 10, 11
10/24 Iterative problems
10/26 Bayes Therom
Week 9 Bayesian Methods Ch 11
10/31 Bayesian inversion Ch 11 bayes_2d_inclass.m
11/02 MCMC Tarantola Ch 2 metropolis.m, pm1m2.m, random_walk_class.m, single_gauss_1D.m.