課程資訊
課程名稱
數值線性代數
Numerical Linear Algebra 
開課學期
102-1 
授課對象
理學院  數學系  
授課教師
王偉仲 
課號
MATH5411 
課程識別碼
221 U4210 
班次
 
學分
全/半年
半年 
必/選修
選修 
上課時間
星期二7,8(14:20~16:20)星期四7(14:20~15:10) 
上課地點
天數201天數201 
備註
總人數上限:30人 
Ceiba 課程網頁
http://ceiba.ntu.edu.tw/1021nla 
課程簡介影片
 
核心能力關聯
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課程大綱
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課程概述

This course covers both basic and state-of-the-art concepts, algorithms, theories, and implementations in numerical linear algebra. Students will learn and practice the subjects from the viewpoints of application, mathematics, and computing. We plan to cover the following topics.

* Fundamentals of scientific computing
   - Floating point arithmetic
   - Perturbation theory
   - Condition number
   - Numerical stability
   - Roundoff error analysis
   - Memory architecture and parallel computer
   - Computation and communication

* Linear systems: direct methods
   - LU decomposition
   - Error analysis (Pivoting and condition number)
   - Blocking algorithms for higher performance
   - Cholesky decomposition for symmetric positive definite matrices
   - Factorization for sparse matrices with reordering

* Least squares problems
   - Normal equations
   - QR decomposition
   - Singular value decomposition (SVD)
   - Orthogonal transformations (Householder, Givens rotations, others)

* Linear systems: iterative methods
   - Stationary iterative methods (Jacobi, Gauss-Seidel, SOR, SSOR)
   - Projection operators
   - Fundamentals of project methods
   - Arnoldo's method
   - Conjugate method (CG)
   - Generalized Minimal Residual (GMRES)
   - Other Krylov methods (BiCG, QMR, CGS, Bi-CGSTAB)
   - Preconditioning techniques

* Eigenvalue problems
   - Rayleigh quotient based methods  

課程目標
The goals of this course are (i) to provide theoretical insight and computational hands-on experience in numerical linear algebra and (ii) to guide students to conduct researches in selected topics. With the training of the course, we expect the students can choose efficient algorithms and software to solve their problems and have enough backgrounds to develop new methods and tools. 
課程要求
Linear Algebra, Programming Language (e.g. MATLAB, C, C++, or CUDA), Introduction to Computational Mathematics 
預期每週課後學習時數
 
Office Hours
 
參考書目
- Matrix Computations, Fourth Edition, Gene H. Golub and Charles F. Van Loan, SIAM, 2013
(http://www.ec-securehost.com/SIAM/JH01.html)
 
指定閱讀
(1) Applied Numerical Linear Algebra, James W. Demmel, SIAM, 1997
(2) Iterative Methods for Sparse Linear Systems, 2nd Edition, Yousef Saad, 2003 (http://www-users.cs.umn.edu/~saad/IterMethBook_2ndEd.pdf)
(3) Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods, 2nd Edition, Richard Barrett et al., SIAM, 1994 
評量方式
(僅供參考)
 
No.
項目
百分比
說明
1. 
Homework and class participance  
30% 
 
2. 
Term project 
40% 
 
3. 
Class notes and concept maps 
30% 
 
 
課程進度
週次
日期
單元主題
第1週
9/10,9/12  Introduction, source of error and error analysis. 
第2週
9/17,9/19  Perturbation analysis, condition number, stability and floating point system. 
第3週
9/24,9/26  Perturbation analysis, relative error and LU decomposition. 
第4週
10/01,10/03  BLAS3 LU decomposition 
第5週
10/08,10/10  Special linear systems, s.p.d. matrices and Cholesky decomposition. 
第6週
10/15,10/17  Cholesky decomposition, sparse matrices, perturbation theory for direct method. 
第8週
10/29,10/31  Linear least square problem (2013/10/29) 
第12週
11/26,11/28  11/28 Roofline model by 周函融&嚴炳欽 
第13週
12/03,12/05  12/03, 12/05 : TIMS Winter School for Scientific Computing 
第17週
12/31,1/02  Conjugate gradient method