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課程名稱 |
數值線性代數
Numerical Linear Algebra |
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開課學期 |
109-1 |
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授課對象 |
理學院 數學研究所 |
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授課教師 |
薛克民 |
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課號 |
MATH5411 |
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課程識別碼 |
221 U4210 |
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班次 |
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學分 |
3.0 |
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全/半年 |
半年 |
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必/選修 |
選修 |
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上課時間 |
星期四2,3,4(9:10~12:10) |
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上課地點 |
天數304 |
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備註 |
總人數上限：40人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1091MATH5411_NLA |
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課程簡介影片 |
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核心能力關聯 |
本課程尚未建立核心能力關連 |
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課程大綱
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為確保您我的權利,請尊重智慧財產權及不得非法影印
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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. |
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課程目標 |
Development, implementation, and analysis of numerical algorithms
for solving system of matrix equations |
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課程要求 |
Linear Algebra & Introduction to Computational Mathematics |
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預期每週課後學習時數 |
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Office Hours |
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指定閱讀 |
待補 |
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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) |
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評量方式
(僅供參考) |
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No. |
項目 |
百分比 |
說明 |
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1. |
Homework |
60% |
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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% |
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週次 |
日期 |
單元主題 |
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第1週 |
09/17 |
Linear algebra (Review) & sample examples |
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第2週 |
09/24 |
LU factorization, & Cholesky factorization
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第3週 |
10/01 |
<font color=#ff0000> No class: 中秋節放假</font> |
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第4週 |
10/08 |
Least squares problems, Gram-Schmidt orthogonalization, Householder triangularization, Givens rotation, minimum-norm solution |
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第5週 |
10/15 |
QR insert, QR delete, rank deficient, conditioning of linear system, conditioning of least squares problems |
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第6週 |
10/22 |
basic iterative linear solvers (splitting, gradient descend),
Arnoldi and Lanczos iterations for Krylov spaces, GMRES, FOM |
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第7週 |
10/29 |
Conjugate gradient method |
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第8週 |
11/05 |
Conjugate gradient method |
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第9週 |
11/12 |
<font color=#0000ff> Midterm
Time: 09:10-12:00
Topics: Week 1-6
Open books and notes </font> |
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第10週 |
11/19 |
<font color=#ff0000> No class: 自我學習週</font>
<font color=#438D80> Term project proposal due </font> |
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第11週 |
11/26 |
Stability of algorithm,
preconditioned conjugate gradient method,
BICG |
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第12週 |
12/03 |
Algebraic eigenvalue problems:
Power iteration & variants, QR algorithm,How Arnoldi locates eigenvalues |
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第13週 |
12/10 |
Singular value decomposition (SVD) |
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第14週 |
12/17 |
Polar decomposition |
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第15週 |
12/24 |
l1-minimization problems & solvers |
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第16週 |
12/31 |
Basic constrained optimization solvers, low rank approximation |
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第17週 |
01/07 |
<font color=#0000ff> Final project presentation </font> |
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