課程資訊
課程名稱
數值線性代數
Numerical Linear Algebra 
開課學期
106-1 
授課對象
理學院  數學研究所  
授課教師
王偉仲 
課號
MATH5411 
課程識別碼
221 U4210 
班次
 
學分
3.0 
全/半年
半年 
必/選修
選修 
上課時間
星期四2,3,4(9:10~12:10) 
上課地點
天數201 
備註
總人數上限:40人 
Ceiba 課程網頁
http://ceiba.ntu.edu.tw/1061MATH5411_ 
課程簡介影片
 
核心能力關聯
本課程尚未建立核心能力關連
課程大綱
為確保您我的權利,請尊重智慧財產權及不得非法影印
課程概述

The course consists of the following four parts.
• Part A. A 75-minute lecture on every Thursday (9:10-10:25) from 2017/9/14 to 2017/12/7.
• Part B. A 75-minute hands-on session on every Thursday (10:35-11:50) from 2017/9/14 to 2017/12/7.
• Part C. An online course that consists of twelve 75-minute lectures by Prof. Edmond Chow. This online course should be self-studied from 2017/9/14 to 2017/11/2.
• Part D. Twelve 75-minute lectures (12:10-13:25) on selected days from 2017/12/18 to 2018/1/5.

The tentative schedule for Parts A, B, C is listed below. The online course of Part C is available on the web page https://sites.google.com/site/school4scicomp/previous/2016-b-spring.

• Week 1 (2017/9/14)
o Lecture
♣ a. Introduction to course
♣ b. Graph Laplaician
♣ c. Applications in 3D face animation and data network analysis
o Hands-on session
♣ a. Download data from http://konect.uni-koblenz.de/
♣ b. Construct the matrices by Matlab or GPU
♣ c. Check the sparsity of the matrices
♣ d. Learn mathematical software tool (web)
o Online course
♣ a. [0503-1], [0503-2], [0505-1]
• Week 2 (2017/9/21)
o Lecture
♣ a. power method for EVP
♣ b. inverse power method for EVP
o Hands-on session
♣ a. Practice mathematical software tools
♣ b. Learn basic CUDA programming
♣ c. Use csreigvsi in cuSolverSP to compute the target eigenvalues
♣ d. Try other problems by using csreigvsi
o Online course
♣ [0505-2], [0506-1], [0506-2]
• Week 3 (2017/9/28)
o Lecture
♣ a. None
o Hands-on session
♣ a. Solve the linear system (A + 1.0e-5 I) y = b by using the direct solvers (LU and Cholesky) in cuSolverSP package to solve the linear systems from http://konect.uni-koblenz.de/ with various dimensions
♣ b. Discuss the results in direct solvers
o On-line course
♣ [0509-1], [0509-2], [0510-1]
• Week 4 (2017/10/5)
o Lecture
♣ a. Conjugate gradient method
o Hnads-on session
♣ a. Learn how to use magma_dcg (Conjugate Gradient method) in MAGMA
o Online course
♣ [0510-2], [0511-1], [0511-2]
• Week 5 (2017/10/12)
o Lecture
♣ a. Conjugate gradient method
o Hands-on session
♣ a. Use magma_dcg type functions in MAGMA to solve linear system from 3D face animation
♣ b. Use magma_dcg type functions in MAGMA to solve linear system from http://konect.uni-koblenz.de/ with various dimensions
o Online course
♣ [0512-1], [0512-2], [0516-1]
• Week 6 (2017/10/19)
o Lecture
♣ a. Preconditioning conjugate gradient method
o Hands-on session
♣ a. Learn how to use PCG with preconditioners in MAGMA
o Online course
♣ [0516-2], [0517-1], [0517-2]
• Week 7 (2017/10/26)
o Lecture
♣ a. Preconditioner
o Hands-on session
♣ a. Use CG method in MAGMA with ICC (magma_dapplycumicc_l) and ILU (magma_dapplycumilu_l and magma_dapplycumilu_r) preconditioners
o Online course
♣ [0518-1], [0518-2], [0519-1], [0519-2]
• Week 8 (2017/11/2)
o Lecture
♣ a. Preconditioner
o Hands-on session
♣ a. Compare the results of CG method in MAGMA with ICC, ILU, and other preconditioners
♣ b. Run AmgX to solve linear systems
• Week 9 (2017/11/9)
o Lecture
♣ a. BiCGSTAB
o Hands-on session
♣ a. Learn how to use un-symmetric linear solvers in MAGMA
• Week 10 (2017/11/16)
o Lecture
♣ a. BiCGSTAB
o Hands-on session
♣ a. Use BiCGSTAB (magma_dbicgstab) with ILU preconditioner to solve linear system (A - 1.0e-5) y = b
• Week 11 (2017/11/23)
o Lecture
♣ a. Lanczos method
o Hands-on session
♣ a. Learn how to use sparse eigensolver in MAGMA
• Week 12 (2017/11/30)
o Lecture
♣ a. Lanczos method
o Hands-on session
♣ a. Use LOBPCG (magma_dlobpcg) to compute the target eigenvalues
• Week 13 (2017/12/7)
o Midterm

The outline of Part D is listed below. See https://sites.google.com/site/school4scicomp/2017-d-chow for more information.
• Krylov subspace methods
o Projection method viewpoint and unifying framework
o Specialized methods
o Avoiding communication and synchronization
o Restarting for eigenvalue solvers
• Hierarchical matrix methods
o Physical intuition and relation to fast multipole methods
o Hierarchical matrix construction and solution methods
• Domain decomposition methods
o Optimized Schwarz methods
o FETI and related methods
• Multigrid methods
o Convergence theory
o Algebraic multigrid
• Parallel Preconditioning
o Advanced ideas on incomplete factorizations
o Advanced ideas on sparse approximate inverses
o Other recent developments
 

課程目標
This course covers some of the most basic and latest concepts, algorithms, theories, and implementations in numerical linear algebra. Students will learn and practice the subjects from the viewpoints of application, mathematics, and parallel computing.  
課程要求
Linear Algebra, Programming Language (e.g. MATLAB, C, C++, or CUDA), Introduction to Computational Mathematics, Calculus 
預期每週課後學習時數
 
Office Hours
另約時間 
參考書目
[1] Numerical Linear Algebra By Lloyd N. Trefethen and David Bau III, SIAM
[2] Applied Numerical Linear Algebra, James W. Demmel, SIAM, 1997
[3] Iterative Methods for Sparse Linear Systems, 2nd Edition, Yousef Saad, 2003 (http://www-users.cs.umn.edu/~saad/IterMethBook_2ndEd.pdf)
[4] Matrix Computations, Fourth Edition, Gene H. Golub and Charles F. Van Loan, SIAM, 2013
[5] Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods, 2nd Edition, Richard Barrett et al., SIAM, 1994
[6] 大型線性系統與特徵值問題 http://ocw.lib.ntnu.edu.tw/course/view.php?id=190  
指定閱讀
Course slides 
評量方式
(僅供參考)
 
No.
項目
百分比
說明
1. 
課堂討論,課堂報告,回家作業 
60% 
 
2. 
期中考 
40% 
 
 
課程進度
週次
日期
單元主題