Topic: LU Factorization and Numerical Considerations

Zero Pivots and Elimination Breakdown

Why Induced Matrix Norms Are Submultiplicative

Vector Norms for Measuring Size

Triangular Solve Costs and Repeated Right-Hand Sides

The LU Factorization Theorem Without Pivoting

Solving Systems With Forward and Back Substitution

Solving Permuted Systems From PA = LU

Small Residuals With Large Solution Errors

Scaling Variables and Equations

Residuals and Forward Error