|
課程名稱 |
數值線性代數
Numerical Linear Algebra |
|
開課學期 |
108-1 |
|
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304 |
|
備註 |
總人數上限：40人 |
|
Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1081MATH5411_ |
|
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 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 |
1. Analysis of numerical algorithms
2. Numerical implementation of algorithm
3. Applications |
|
課程要求 |
Linear Algebra & Introduction to Computational Mathematics |
|
預期每週課後學習時數 |
|
|
Office Hours |
另約時間 |
|
指定閱讀 |
L. Elden, Matrix Methods in data mining and pattern recognition, 2007 , ebook (see bulletin board) |
|
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 |
|
評量方式
(僅供參考) |
|
No. |
項目 |
百分比 |
說明 |
|
1. |
Midterm exam |
25% |
Time: 09:10-12:10, 11/07
Topics: TBA
Open book & notes |
2. |
Final exam |
25% |
Time: 09:10-12:10, 01/02
Topics: TBA
Open book & notes |
3. |
Homework |
50% |
|
|
|
週次 |
日期 |
單元主題 |
|
第1週 |
09/12 |
Overview, examples, linear algebra review (vectors, matrices, norms) |
|
第2週 |
09/19 |
請假 |
|
第3週 |
09/26 |
QR factorization: Gram-Schmidt process, Householder triangularization, Givens rotations,
& QR insert, delete |
|
第4週 |
10/03 |
Least-squares problems |
|
第5週 |
10/10 |
<font color=#ff0000> No class: 國慶日 </font> |
|
第6週 |
10/17 |
Conditioning of problems, stability of algorithms,
LU & Cholesky factorization |
|
第7週 |
10/24 |
Tridiagonal & periodic tridiagonal linear systems |
|
第8週 |
10/31 |
Iterative methods for linear systems |
|
第9週 |
11/07 |
GMRES algorithm |
|
第10週 |
11/14 |
CG algorithm & PCG |
|
第11週 |
11/21 |
PCG & BICG |
|
第12週 |
11/28 |
BICG, Power's method & its variant |
|
第13週 |
12/05 |
QR algorithm |
|
第14週 |
12/12 |
SVD & ISTA |
|
第15週 |
12/19 |
出國開會請假 |
|
第16週 |
12/26 |
Singular value thresholding algorithm, quasi-Newton method |
|
第17週 |
1/02 |
<font color=#0000ff> Take home final exam </font> |
|