This code was presented by the professor in order to facilitate the learning process and assist in the better understanding of the course material.

LEC # | TOPICS | TOOLS |
---|---|---|

1 | Introduction | EppBAP.mat (MAT) |

2 | The Condition Number | airfoil1.mat (MAT) |

3 | The Largest Singular Value of a Matrix | airfoil2.mat (MAT) |

4 | Gaussian Elimination Without Pivoting | art.m (M) |

5 | Smoothed Analysis of Gaussian Elimination Without Pivoting | art3.m (M) |

6 |
Growth Factors of Partial and Complete Pivoting Speeding up GE of Graphs with Low Bandwidth or Small Separators |
chew_circle.mat (MAT) convert.m (M) |

7 | Spectral Partitioning Introduced | crossedGrid.m (M) |

8 | Spectral Partitioning of Planar Graphs | dat.mat (MAT) |

9 |
Spectral Paritioning of Well-Shaped Meshes and Nearest Neighbor Graphs Turner’s Theorem for Bandwidth of Semi-Random Graphs |
epp.mat (MAT) eppstein.mat (MAT) |

10 |
Smoothed Analysis and Monotone Adversaries for Bandwidth and Graph Bisection McSherry’s Spectral Bisection Algorithm |
fastfiedler.m (M) gauss.m (M) |

11 |
Introduction to Linear Programming von Neumann’s Algorithm, Primal and Dual Simplex Methods Duality |
graph2A.m (M) kahan.m (M) kahan2.m (M) |

12 |
Strong Duality Theorem of Linear Programming Renegar’s Condition Numbers |
laplacian.m (M) mcrack.mat (MAT) |

13 | Analysis of von Neumann’s Algorithm | n.mat (MAT) |

14 | Worst-Case Complexity of the Implex Method | noPivot.m (M) |

15 | The Expected Number of Facets of the Convex Hull of Gaussian Random Points in the Plane | ppConj.m (M) |

16 | The Expected Number of Facets of the Convex Hull of Gaussian Random Points in the Plane (cont.) | ppDat.mat (MAT) |

17 | The Expected Number of Facets of the Shadow of a polytope Given by Gaussian random Constraints | spectShow.m (M) |

18 | The Expected Number of Facets of the Shadow of a Polytope Given by Gaussian Random Constraints: Distance Bound | spectShow1.m (M) |

19 | The Expected Number of Facets of the Shadow of a Polytope Given by Gaussian Random Constraints: Angle Bound and Overview of Phase 1 | v4.mat (MAT) |