課程: 大型線性系統與特徵值問題/台大數學系教授

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1	Chapter 1: Introduction (課程影音) SCORM/AICC 課程包 Chapter 1: Introduction (課程講義) PDF 文件一、Vectors and matrices 檔案二、Eigenvalues and Eigenvectors 檔案三、Norms and eigenvalues 檔案四、Backward error and Forward error（一）檔案五、Backward error and Forward error（二）檔案

2	Chapter 2:Gaussian Elimination for Linear Systems (課程影音) SCORM/AICC 課程包 Chapter 2:Gaussian Elimination for Linear Systems (課程講義) PDF 文件一、Error analysis for Gaussian algorithm 檔案

3	Iterative Methods for Solving Large Linear Systems (課程影音) SCORM/AICC 課程包 Iterative Methods for Solving Large Linear Systems (課程講義) PDF 文件 Iterative Methods for Solving Large Linear Systems 檔案一、General procedures for the construction of iterative methods 檔案二、Determination of the Optimal Parameter ω for 2-consistly Ordered Matrices 檔案

4	Conjugate Gradient Method (課程影音) SCORM/AICC 課程包 Conjugate Gradient Method (課程講義) PDF 文件一、A Variational Problem, Steepest Descent Method 檔案二、Conjugate gradient method 檔案三、Practical Implementation 檔案四、Convergence of CG-method 檔案

5	GCG-type Methods for Nonsymmetric Linear Systems (課程影音) SCORM/AICC 課程包 GCG-type Methods for Nonsymmetric Linear Systems(課程講義) PDF 文件 GCG-type Methods for Nonsymmetric Linear Systems 檔案一、GCG method(Generalized Conjugate Gradient) 檔案二、BCG method (A: unsymmetric) 檔案三、The polynomial equivalent method of the CG method 檔案四、Bi-CGSTAB(SISC, 1992, Van der Vorst) 檔案

6	GMRES: Generalized Minimal Residual Algorithm forSolving Nonsymmetric Linear Systems(課程影音) SCORM/AICC 課程包 GMRES: Generalized Minimal Residual Algorithm forSolving Nonsymmetric Linear Systems (課程講義) PDF 文件 GMRES: Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems 檔案一、The generalized minimal residual (GMRES) algorithm 檔案

7	CG-Method as an Iterative Method, Preconditioning (課程影音) SCORM/AICC 課程包 CG-Method as an Iterative Method, Preconditioning (課程講義) PDF 文件 CG-Method as an Iterative Method, Preconditioning 檔案一、A new point of view of PCG 檔案二、Chebychev Semi-Iteration Acceleration Method 檔案三、Some theorems and definitions 檔案四、Sufficient conditions for convergence of TSM and SSM 檔案五、Incomplete Cholesky Decomposition 檔案

8	Recent Advance in Numerical Algorithms for Large/Sparse Eigenvalue Problems (課程影音) SCORM/AICC 課程包 Recent Advance in Numerical Algorithms for Large/Sparse Eigenvalue Problems (課程講義) PDF 文件 Recent Advance in Numerical Algorithms for Large/Sparse Eigenvalue Problems 檔案一、Power Methods 檔案二、Inverse Power Iteration 檔案三、Connection with Newton method 檔案

9	Krylov Subspace Methods for Large/Sparse Eigenvalue Problems (I) (課程影音) SCORM/AICC 課程包 Krylov Subspace Methods for Large/Sparse Eigenvalue Problems (I) (課程講義) PDF 文件 Krylov Subspace Methods for Large/Sparse Eigenvalue Problems (I) 檔案一、Orthogonal projection methods 檔案二、Krylov Subspaces 檔案三、Householder transformation 檔案四、Arnoldi Method 檔案

10	Krylov Subspace Methods for Large/Sparse Eigenvalue Problems (II) (課程影音) SCORM/AICC 課程包 Krylov Subspace Methods for Large/Sparse Eigenvalue Problems (II) (課程講義) PDF 文件 Krylov Subspace Methods for Large/Sparse Eigenvalue Problems (II) 檔案一、Restarting method 檔案二、Generalized eigenvalue problem 檔案

11	Polynomial Jacobi Davidson Method for Large/Sparse Eigenvalue Problems (課程影音) SCORM/AICC 課程包 Polynomial Jacobi Davidson Method for Large/Sparse Eigenvalue Problems (課程講義) PDF 文件 Polynomial Jacobi Davidson Method for Large/Sparse Eigenvalue Problems 檔案一、Jacobi’s orthogonal component correction, 1846 檔案二、Davidson’s method (1975) 檔案三、Jacobi-Davidson method (1996) 檔案四、Polynomial Jacobi-Davidson method 檔案五、Non-equivalence deflation of quadratic eigenproblems 檔案

12	QR Algorithm for Dense Eigenvalue Problems (課程影音) SCORM/AICC 課程包 QR Algorithm for Dense Eigenvalue Problems (課程講義) PDF 文件 QR Algorithm for Dense Eigenvalue Problems 檔案一、QR Algorithm 檔案二、The Practical QR Algorithm 檔案三、Single-shift QR-iteration 檔案四、Double Shift QR iteration 檔案