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| 1 | Chapter 1: Introduction (課程講義) | |
| 一、Vectors and matrices | |
| 二、Eigenvalues and Eigenvectors | |
| 三、Norms and eigenvalues | |
| 四、Backward error and Forward error（一） | |
| 五、Backward error and Forward error（二） | |
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| 2 | Chapter 2:Gaussian Elimination for Linear Systems (課程講義) | |
| 一、Error analysis for Gaussian algorithm | |
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| 3 | Iterative Methods for Solving Large Linear Systems (課程講義) | |
| Iterative Methods for Solving Large Linear Systems | |
| 一、General procedures for the construction of iterative methods | |
| 二、Determination of the Optimal Parameter ω for 2-consistly Ordered Matrices | |
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| 4 | Conjugate Gradient Method (課程講義) | |
| 一、A Variational Problem, Steepest Descent Method | |
| 二、Conjugate gradient method | |
| 三、Practical Implementation | |
| 四、Convergence of CG-method | |
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| 5 | GCG-type Methods for Nonsymmetric Linear Systems(課程講義) | |
| GCG-type Methods for Nonsymmetric Linear Systems | |
| 一、GCG method(Generalized Conjugate Gradient) | |
| 二、BCG method (A: unsymmetric) | |
| 三、The polynomial equivalent method of the CG method | |
| 四、Bi-CGSTAB(SISC, 1992, Van der Vorst) | |
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| 6 | GMRES: Generalized Minimal Residual Algorithm forSolving Nonsymmetric Linear Systems (課程講義) | |
| GMRES: Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems | |
| 一、The generalized minimal residual (GMRES) algorithm | |
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| 7 | CG-Method as an Iterative Method, Preconditioning (課程講義) | |
| CG-Method as an Iterative Method, Preconditioning | |
| 一、A new point of view of PCG | |
| 二、Chebychev Semi-Iteration Acceleration Method | |
| 三、Some theorems and definitions | |
| 四、Sufficient conditions for convergence of TSM and SSM | |
| 五、Incomplete Cholesky Decomposition | |
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| 8 | Recent Advance in Numerical Algorithms for Large/Sparse Eigenvalue Problems (課程講義) | |
| Recent Advance in Numerical Algorithms for Large/Sparse Eigenvalue Problems | |
| 一、Power Methods | |
| 二、Inverse Power Iteration | |
| 三、Connection with Newton method | |
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| 9 | Krylov Subspace Methods for Large/Sparse Eigenvalue Problems (I) (課程講義) | |
| Krylov Subspace Methods for Large/Sparse Eigenvalue Problems (I) | |
| 一、Orthogonal projection methods | |
| 二、Krylov Subspaces | |
| 三、Householder transformation | |
| 四、Arnoldi Method | |
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| 10 | Krylov Subspace Methods for Large/Sparse Eigenvalue Problems (II) (課程講義) | |
| Krylov Subspace Methods for Large/Sparse Eigenvalue Problems (II) | |
| 一、Restarting method | |
| 二、Generalized eigenvalue problem | |
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| 11 | Polynomial Jacobi Davidson Method for Large/Sparse Eigenvalue Problems (課程講義) | |
| Polynomial Jacobi Davidson Method for Large/Sparse Eigenvalue Problems | |
| 一、Jacobi’s orthogonal component correction, 1846 | |
| 二、Davidson’s method (1975) | |
| 三、Jacobi-Davidson method (1996) | |
| 四、Polynomial Jacobi-Davidson method | |
| 五、Non-equivalence deflation of quadratic eigenproblems | |
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| 12 | QR Algorithm for Dense Eigenvalue Problems (課程講義) | |
| QR Algorithm for Dense Eigenvalue Problems | |
| 一、QR Algorithm | |
| 二、The Practical QR Algorithm | |
| 三、Single-shift QR-iteration | |
| 四、Double Shift QR iteration | |