LEC # | TOPICS |
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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 |

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*notes*Lecture Notes