課程資訊
課程名稱
數值線性代數
Numerical Linear Algebra 
開課學期
104-1 
授課對象
理學院  應用數學科學研究所  
授課教師
王偉仲 
課號
MATH5411 
課程識別碼
221 U4210 
班次
 
學分
全/半年
半年 
必/選修
必修 
上課時間
星期二7,8(14:20~16:20)星期四7,8(14:20~16:20) 
上課地點
天數430天數430 
備註
總人數上限:13人 
Ceiba 課程網頁
http://ceiba.ntu.edu.tw/1041nla 
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

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This course covers 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 (four subspaces, matrix-vector multiplication, orthogonal vector, norms, projection, sparse matrix, conditioning, stability)
- Linear systems (Gaussian elimination, pivoting, Cholesky decomposition, stationary iterative methods, Krylov subspace methods)
- Eigenvalue problems (Reduction to Hessenberg and tridiagonal form, Rayleigh quotient and inverse iteration, QR, Jacobi-Davidson, Shift-and-Invert Residual, Arnoldi, contour integral
- Singular value decomposition
- Least square problems (normal equations, QR decomposition, Gram-Schmidt orthogonalization, Householder transformations, Givens rotation)
 

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++, and/or CUDA), Introduction to Computational Mathematics, Calculus 
預期每週課後學習時數
 
Office Hours
 
參考書目
- Applied Numerical Linear Algebra, James W. Demmel, SIAM, 1997
- Iterative Methods for Sparse Linear Systems, 2nd Edition, Yousef Saad, 2003 (http://www-users.cs.umn.edu/~saad/IterMethBook_2ndEd.pdf)
- Matrix Computations, Fourth Edition, Gene H. Golub and Charles F. Van Loan, SIAM, 2013
- Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods, 2nd Edition, Richard Barrett et al., SIAM, 1994

- G. Allaire and S. M. Kaber, Numerical Linear Algebra, Springer 2008. (e-book)
- A. Greenbaum, Iterative Methods for Solving Linear Systems, SIAM 1997.
- H. A. van der Vorst, Iterative Methods for Large Linear Systems, 2002. (e-
book)
 
指定閱讀
L. N. Trefethen and D. Bau, III, Numerical Linear Algebra, SIAM 1997. (e-book)  
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,上課表現 
20% 
 
2. 
期中考 
40% 
 
3. 
期末考 
40% 
 
 
課程進度
週次
日期
單元主題