I ON THE NUMERICAL SOLUTIONS OF LINEAR SYSTEMS
1. INTRODUCTION
．Mathematical Auxiliary, Definitions and Relations
．Norms and Eigenvalues
．The Sensitivity of Linear System AX = B
2. NUMERICAL METHODS FOR SOLVING LINEAR SYSTEMS
．Elementary matrices
．LR-Factorization
．Gaussian Elimination
．Special linear System
3. ORTHOGONALIZATION AND LEAST SQUARES METHODS
．QR-Factorization (QR-Decomposition)
．Overdetermined Linear Systems - Least Squares methods
4. ITERATIVE METHODS FOR SOLVING LARGE LINEAR SYSTEMS
．General procedures for the Construction of Iterative Methods
．Relaxation Methods (Successive Over-Relaxation (SOR) Method )
．Application to Finite Difference Methods: Model Problem (Example 4.1.3)
．Block Iterative Methods
．The ADI Method of Peaceman and Rachford
．Derivation and Properties of the Conjugate Gradient Method
．CG-Method as an Iterative Method, Preconditioning
．Incomplete Cholesky Decomposition
．Chebychev Semi-Iteration Acceleration Method
．GCG-Type Methods for Nonsymmetric Linear Systems
．CGS (Conjugate Gradient Squared), a Fast Lanczos-Type Solver for Nonsymmetric Linear Systems
．BI-CGSTAB: A fast and Smoothly Converging Variant of BI-CG for the Solution of Nonsymmetric Linear Systems
．A Transpose-Free Qusi-Minimal Residual Algorithm for Nonsymmetric Linear Systems
．GMRES: Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
II ON THE NUMERICAL SOLUTIONS OF EIGENVALUE PROBLEMS
5. THE UNSYMMETRIC EIGENVALUE PROBLEM
．Orthogonal Projections and C-S Decomposition
．Perturbation Theory
．Power Iterations
．QR-Algorithm (QR-Method, QR-Iteration)
．LR, LRC AND QR Algorithms for Positive Definite Matrices
．QD-Algorithm (Quotient Difference)