|
課程名稱 |
數值線性代數
Numerical Linear Algebra |
|
開課學期 |
107-1 |
|
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/1071MATH5411_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
|
|
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 |
|
課程目標 |
1. Theoretical analysis of the numerical algorithms
2. Numerical implementation of the algorithms
3. Applications |
|
課程要求 |
Linear Algebra & Introduction to Computational Mathematics |
|
預期每週課後學習時數 |
|
|
Office Hours |
每週三 14:00~15:00 |
|
指定閱讀 |
待補 |
|
參考書目 |
1. Numerical Linear Algebra By Lloyd N. Trefethen and David Bau III, SIAM
2. Applied Numerical Linear Algebra, James W. Demmel, SIAM, 1997
3. Iterative Methods for Sparse Linear Systems, 2nd Edition, Yousef Saad, 2003
(http://www-users.cs.umn.edu/~saad/IterMethBook_2ndEd.pdf)
4. Matrix Computations, Fourth Edition, Gene H. Golub and Charles F. Van Loan,
SIAM, 2013
5. 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. |
Midterm exam |
25% |
|
2. |
Final exam |
25% |
|
3. |
Homework |
50% |
|
|
|
週次 |
日期 |
單元主題 |
|
第1週 |
09/13 |
Course overview |
|
第2週 |
09/20 |
Linear algebra review: vectors, matrices, & norms;
example fo underdetermined linear system of equations |
|
第3週 |
09/27 |
SVD & four fundamental spaces |
|
第4週 |
10/04 |
QR factorization: Gram-Schmidt & modified Gram-Schmidt process |
|
第5週 |
10/11 |
QR facorization: Householder triangularization & Givens rotation
Least square problems |
|
第6週 |
10/18 |
QR delete, insert, update |
|
第7週 |
10/25 |
Conditioning of problems &
stability of algorithms |
|
第8週 |
11/01 |
Stability of algorithm, LU & Cholesky factorization |
|
第9週 |
11/08 |
<font color=#0000ff> Midterm exam </font> |
|
第10週 |
11/15 |
<font color=#ff0000> No class: 校慶 </font> |
|
第11週 |
11/22 |
Eigenvalue problems: Model examples, Basic linear algebra revisit
QR algorithm (first view), Power method \& its variant |
|
第12週 |
11/29 |
QR algorithms, Krylov subspaces & Arnoldi iteration |
|
第13週 |
12/06 |
Computing SVD |
|
第14週 |
12/13 |
Arnoldi iteration & polynomial approximation |
|
第15週 |
12/20 |
GMRES, polynomial approximation, & basic iterative methods |
|
第16週 |
12/27 |
Conjugate gradient algorithm |
|
第17週 |
1/03 |
BiCG
method for non-symmetric systems |
|
第18週 |
01/10 |
<font color=#0000ff> Final exam </font> |
|