Abstract : 「矩陣計算」是計算科學中一個重要的核心工具。此系列課程將針對大型的線性系統與特徵值問題兩大主題，以統合的觀點（線性系統與特徵值分別以 PCG 與 Arnoldi 為主要方法），闡述傳統與近代發展的計算理論與計算方法，以期在短期內對此主題的整體架構，有全面且深入的了解。

Instructor : Wen-Wei Lin

• NTNU Open Course(go)

Large-scale Linear System Problems

• Introduction [ view course PPT ]
• Gaussian Elimination for Linear Systems [ view course PPT ]

Video: v01, v02, v03, v04, v05, v06

• Iterative Methods for Solving Large Linear Systems [ view course PPT ]
• Conjugate Gradient Method [ view course PPT ]
• CG Method as an Iterative Method and Preconditioning [ view course PPT ]

Video:

v2-1 [26:37] >> Review of GE, s04a: p1-8

v2-2 [25:39] >> s04a: p20-28

v2-3 [23:03] >> s04a: p29-38, s04b: p1-14 [10:30-23:03]

v2-4 [28:11] >> s04b: p14-32

v2-5 [17:24] >> s04c: p1-8

v2-6 [18:10] >> s04c: p9-16

• Generalized Conjugate Gradient Methods for Non-symmetric Linear Systems [ view course PPT ] (s04d)

Video:

v3-1 [21:21] >> Review of PCG, s04d: p1-8 [05:53-21:21]

v3-2 [23:17] >> s04d: p9-

v3-3

v3-4

• GMRES: Generalized Minimal Residual Algorithm for Solving Non-symmetric Linear Systems [ view course PPT ] (s04c)

Video:v3-5, v3-6

• CG Method as an Iterative Method and Preconditioning [ view course PPT ] (s04c)

Video:v01, v02, v03, v04

• Applications and Numerical Experiences (by Prof. Tsung-Ming Huang)

Video: v05, v06

Large-scale Eigenvalue Problems

• Power and QR Methods (s05)
• Power methods
• Inverse power methods

Video: v01,v02

• Krylov Subspace Methods (s06)
• Orthogonal projection methods
• Krylov Subspaces

Video:v03

• Householder transformation

Video:v04

• Arnoldi and Lanczos methods

Video:v05, v06

• Generalized eigenvalue problem
• Implicit-Restart method
• Polynomial Jacobi-Davidson Method (s07)

Video: v01, v02, v03,Polynomial Jacobi-Davidson Method:v04, v05

Dense Eigenvalue Problems

• QR Algorithms (s08)

Video: v01, v02, v03, v04