課程資訊
課程名稱
數值線性代數
Numerical Linear Algebra 
開課學期
109-1 
授課對象
理學院  數學研究所  
授課教師
薛克民 
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304 
備註
總人數上限:40人 
Ceiba 課程網頁
http://ceiba.ntu.edu.tw/1091MATH5411_NLA 
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
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課程概述

The aim of this course is to discuss numerical techniques for solving large linear system of
equations and eigenvalue problems.

Topics to be covered will include:

1. Basic linear algebra (review)
2. QR factorization/least-squares problems
3. Singular value decomposition (SVD)
4. Conditioning & stability
5. Gaussian elimination, pivoting
6. Eigenvalue problems
7. Iterative methods

Continuation of this course to next semester will be on numerical methods for PDEs. 

課程目標
Development, implementation, and analysis of numerical algorithms
for solving system of matrix equations 
課程要求
Linear Algebra & Introduction to Computational Mathematics 
預期每週課後學習時數
 
Office Hours
 
參考書目
1. G. Allaire and S. M. Kaber, Numerical Linear Algebra, Springer 2008. (e-book)
2. J. W. Demmel, Applied Numerical Linear Algebra, SIAM 1997.
3. G. H. Golub and C. F. Van Loan, Matrix Computations, 4rd edition
4. A. Greenbaum, Iterative Methods for Solving Linear Systems, SIAM 1997.
5. L. N. Trefethen and D. Bau, III, Numerical Linear Algebra, SIAM 1997. (e-
book)
6. H. A. van der Vorst, Iterative Methods for Large Linear Systems, 2002. (e-
book)
7. G. Strang, Linear algebra and learning from data, 2019
8. W. Ford, Numerical linear algebra with applications using Matlab, 2014 (e-book) 
指定閱讀
待補 
評量方式
(僅供參考)
 
No.
項目
百分比
說明
1. 
Homework 
60% 
 
2. 
Midterm exam 
20% 
Time: 09:10-12:00, 11/09 Topics: TBA Open books and notes 
3. 
Final term project 
20% 
Written report 15% Presentation 5% 
 
課程進度
週次
日期
單元主題
第1週
09/17  Linear algebra (Review) & sample examples 
第2週
09/24  LU factorization, & Cholesky factorization
 
第3週
10/01  <font color=#ff0000> No class: 中秋節放假</font>  
第4週
10/08  Least squares problems, Gram-Schmidt orthogonalization, Householder triangularization, Givens rotation, minimum-norm solution 
第5週
10/15  QR insert, QR delete, rank deficient, conditioning of linear system, conditioning of least squares problems  
第6週
10/22  basic iterative linear solvers (splitting, gradient descend),
Arnoldi and Lanczos iterations for Krylov spaces, GMRES, FOM 
第7週
10/29  Conjugate gradient method 
第8週
11/05  Conjugate gradient method 
第9週
11/12  <font color=#0000ff> Midterm
Time: 09:10-12:00
Topics: Week 1-6
Open books and notes </font> 
第10週
11/19  <font color=#ff0000> No class: 自我學習週</font>
<font color=#438D80> Term project proposal due </font> 
第11週
11/26  Stability of algorithm,
preconditioned conjugate gradient method,
BICG 
第12週
12/03  Algebraic eigenvalue problems:
Power iteration & variants, QR algorithm,How Arnoldi locates eigenvalues 
第13週
12/10  Singular value decomposition (SVD) 
第14週
12/17  Polar decomposition 
第15週
12/24  l1-minimization problems & solvers 
第16週
12/31  Basic constrained optimization solvers, low rank approximation 
第17週
01/07  <font color=#0000ff> Final project presentation </font>