| LEC # | TOPICS |
|---|---|
| 1 | Introduction |
| 2 | The Condition Number |
| 3 | The Largest Singular Value of a Matrix |
| 4 | Gaussian Elimination without Pivoting |
| 5 | Smoothed Analysis of Gaussian Elimination without Pivoting |
| 6 |
Growth Factors of Partial and Complete Pivoting Speeding up GE of Graphs with Low Bandwidth or Small Separators |
| 7 | Spectral Partitioning Introduced |
| 8 | Spectral Partitioning of Planar Graphs |
| 9 |
Spectral Paritioning of Well-Shaped Meshes and Nearest Neighbor Graphs Turner's Theorem for Bandwidth of Semi-Random Graphs |
| 10 |
Smoothed Analysis and Monotone Adversaries for Bandwidth and Graph Bisection McSherry's Spectral Bisection Algorithm |
| 11 |
Introduction to Linear Programming von Neumann's Algorithm, Primal and Dual Simplex Methods Duality |
| 12 |
Strong Duality Theorem of Linear Programming Renegar's Condition Numbers |
| 13 | Analysis of von Neumann's Algorithm |
| 14 | Worst-Case Complexity of the Simplex Method |
| 15 | The Expected Number of Facets of the Convex Hull of Gaussian Random Points in the Plane |
| 16 | The Expected Number of Facets of the Convex Hull of Gaussian Random Points in the Plane (cont.) |
| 17 | The Expected Number of Facets of the Shadow of a Polytope given by Gaussian Random Constraints |
| 18 | The Expected Number of Facets of the Shadow of a Polytope given by Gaussian Random Constraints: Distance Bound |
| 19 | The Expected Number of Facets of the Shadow of a Polytope given by Gaussian Random Constraints: Angle Bound and Overview of Phase 1 |