| 1 |
Introduction
Content of the Course |
| 2 |
Examples of Inverse Problems, Static and Time Dependent |
| 3 |
Basic Vector/Matrix Notation
Algebraic Formulation |
| 4-6 |
Over/Underdetermined Problems
Varieties of Least-Squares |
| 7 |
Basic Statistics
Concepts and Notation |
| 8 |
Variances/Covariances
Biases of Solutions |
| 9 |
Special Case of Eigenvector Solutions |
| 10-11 |
Singular Value Decomposition and Singular Vector Solutions |
| 12-13 |
Recursive Least-Squares
Gauss-Markov Estimation; Recursive Estimation |
| 14 |
Time-dependent Models
Whole Domain Least-Squares |
| 15-16 |
Sequential Methods (Kalman Filter/RTS Smoother) |
| 16-17 |
Control Problems
Lagrange Multiplier (adjoint) Methods
Non-linear Problems |
| 18 |
Stationary Processes
Numerical Fourier Series/Transforms; Delta Functions |
| 19 |
Statistics of Fourier Representations
Sampling
Periodograms |
| 20 |
Convolution
Power Density Spectral Estimates |
| 21 |
Coherence; Multiple Linear Regression |
| 22 |
Filtering, Prediction Problems |
| 23-24 |
Special Topics, Spillover |