LECTURE 8:SPARSE MATRIX TECHNIQUES FOR LP1. Sparsity

2. Storage and execution operations

3. Minimal degree reordering algorithm

4. Band and envelope methods

Sparse matrix

Bottleneck for Solving LP

Basic Concepts

Basic Concepts

Example

Reducing Fill-ins

Minimum Degree Reordering Algorithm

Example

Example

Minimum Degree Reordering Algorithm

Question

Band Method

Example

Properties of Band

Question

Properties of Envelope

Example

Envelope Ordering Method

Example

Cuthill-McKee scheme

Reverse Cuthill-McKee scheme

Reverse Cuthill-McKee scheme

Example

Example

Example

Example

Example

Reverse Cuthill-McKee scheme

RCM - starting node

Peripheral node

Pseudo-peripheral node finding algorithm