Topic: LU Factorization and Numerical Considerations

Pivot Growth and Practical Pivot Choices

Partial Pivoting and Permutation Matrices

Matrix Norms for Measuring Amplification

Leading Principal Minors and No-Pivot Breakdown

L and U as Records of Elimination

Ill-Conditioning in Nearly Dependent Systems

Gaussian Elimination as Matrix Factorization

Floating-Point Arithmetic and Rounding

Deriving the Jacobi Iteration

Deriving the Gauss-Seidel Iteration