Inverse Problems and Super-Resolution
A graduate course on the mathematical theory and practice of inverse problems, with a special focus on super-resolution. Topics include well-posedness, regularization, Fourier analysis, sparse recovery, ℓ¹ minimization, and parametric (Prony-type) methods.
Lecture notes (Tel Aviv University, Fall 2022):
1. Introduction · 2. Well-Posedness and Stability · 3. Regularization · 4. Practical Aspects · 5. Fourier Analysis · 6. Super-Resolution: Introduction · 7. Sparsity: Introduction · 8. Super-Resolution via ℓ¹ Minimization · 9. Parametric Super-Resolution · 10. Parametric Min-Max Bounds — off-grid, on-grid · 11. Parametric Methods
Numerical Analysis
An undergraduate course covering classical topics in numerical analysis: floating-point arithmetic, interpolation, numerical differentiation and integration, least squares, ODEs, nonlinear equations, and iterative methods for linear systems.
Lecture notes (Tel Aviv University, Spring 2021):
1. Errors and Floating-Point Arithmetic · 2. Interpolation · 3. Numerical Differentiation · 4. Numerical Integration · 5. Gaussian Quadrature · 6. Least Squares · 7. ODEs: One-Step Methods · 8. ODEs: Multistep and Implicit Methods · 9. Nonlinear Equations · 10. Linear Systems: Iterative Methods