課程資訊
課程名稱
數值線性代數
Numerical Linear Algebra 
開課學期
111-1 
授課對象
理學院  應用數學科學研究所  
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
必修 
上課時間
星期四2,3,4(9:10~12:10) 
上課地點
天數305 
備註
總人數上限:40人 
 
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 and stability
5. Gaussian elimination, pivoting
6. Eigenvalue problems
7. Iterative methods
8. Special topics in data science 

課程目標
Development, implementation, and analysis of numerical algorithms
for solving system of matrix equations 
課程要求
Linear Algebra and Introduction to Computational Mathematics 
預期每週課後學習時數
 
Office Hours
每週三 16:00~17:00 
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)
9. D. Cavetti and E. Somersalo, Mathematics of data science: A computational approach to clustering and classification, SIAM
10. N. Gillis, Nonnegative matrix factorization, SIAM 2021 (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 
30% 
Time: 09:10-12:10,11/10 Topics: TBA Open books and notes 
3. 
Final term project 
10% 
Written term report, due 22:00, 12/28 
 
課程進度
週次
日期
單元主題
第1週
09/08  course overview, linear algebra review 
第2週
09/15  projectors, singular value decomposition, least squares problems
 
第3週
09/22  QR factorization, conditioning of linear systems 
第4週
09/29  conditioning of least squares problems 
第8週
10/27   
第10週
11/10  Midterm
Time: 09:10-12:00
Topics: Week 1-8
Open books and notes 
第11週
11/17  No class: Self-learning week
Term project proposal due 
第16週
12/22  22:00, 12/23, Written term report due