大型線性系統與特徵值問題/台大數學系教授

課程資訊
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）

課程資訊
一、Error analysis for Gaussian algorithm

課程資訊
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

課程資訊
一、A Variational Problem, Steepest Descent Method
二、Conjugate gradient method
三、Practical Implementation
四、Convergence of CG-method

課程資訊
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)

課程資訊
GMRES: Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
一、The generalized minimal residual (GMRES) algorithm

課程資訊
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

課程資訊
Recent Advance in Numerical Algorithms for Large/Sparse Eigenvalue Problems
一、Power Methods
二、Inverse Power Iteration
三、Connection with Newton method

課程資訊
Krylov Subspace Methods for Large/Sparse Eigenvalue Problems (I)
一、Orthogonal projection methods
二、Krylov Subspaces
三、Householder transformation
四、Arnoldi Method

課程資訊
Krylov Subspace Methods for Large/Sparse Eigenvalue Problems (II)
一、Restarting method
二、Generalized eigenvalue problem

課程資訊
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