Contents

• 1.1. Matrices
• 1.2. Vectors
• 1.3. Partitioning Matrices and Vectors

Chapter 2. Matrix Analysis

• 2.1. Basic Linear Algebra
• 2.2. Basis, Nullspace, Rank
• 2.3. Matrix Inverse
• 2.4. Determinant
• 2.5. Vector Norms
• 2.6. Absolute/Relative Errors
• 2.7. Convergence
• 2.8. Matrix norms

• 2.9. Some Matrix Norm Properties
• 2.10. The Matrix 2-Norm
• 2.11. Perturbations and the Inverse

Chapter 3. Finite Precision Matrix Computations

• 3.1. Floating Point Numbers
• 3.2 A Model of Flotaing Point Arithmetic

• 3.3. Cancellation
• 3.4. Condition of Linear Systems

Chapter 4. General Linear Systems

• 4.1. Triangular Systems

• 4.2. Elementary Gaussian Transformation
• 4.3. Reduction to Triangular Form
• 4.4. Solving a Linear System
• 4.5. Roundoff Analysis

• 4.6. Pivoting

Chapter 5. Sparse Linear Systems

• 5.1. Banded matrices
• 5.2. Sparse Matrices

• 5.2. Sparse Matrices
• 5.3. A Simple Sparse LU Decomposition Approach

• 5.4. Preprocessing Sparse Matrices
  MATLAB Demo for Maximum Weight Matching. (requires additional software packages ILUPACK and PARDISO)
  A bigger sample matrix
• 5.5. Symmetric Reordering Techniques
  • 5.5.1 Reverse Cuthill-McKee Reordering
    MATLAB Demo and data

• 5.5. Symmetric Reordering Techniques
  • 5.5.1 Reverse Cuthill-McKee Reordering (contd.)
  • 5.5.2 Minimum Degree Reordering
    MATLAB Demo
  • 5.5.3 Multilevel Nested Dissection

• 6.1. The Elimination Tree

• 6.1. The Elimination Tree (contd)
• 6.2. Supernodes
• 6.3. Software and Applications

MATLAB Demo, unsymmetric case, MATLAB Demo, symmetric case

• 7.1. Discretization of PDEs
• 7.2. ILUs

• 8.1. Basic Iterative Methods
• 8.2. Conjugate gradients

MATLAB Demo on iterative methods (Jacobi, Gauss-Seidel, ILU, steepest descent), sample matrix

• 8.2. Conjguate gradients (contd.)

MATLAB Demo on iterative methods (cg, cg precd. by ILU)
Chapter 9. Multigrid Methods

• 9.1. Failure of Standard Methods
• 9.2. Smoothing Analysis
• 9.3. Multigrid Construction