# Tools

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)