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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 |
111-1 |
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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305 |
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備註 |
總人數上限：40人 |
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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 and stability
5. Gaussian elimination, pivoting
6. Eigenvalue problems
7. Iterative methods
8. Special topics in data science |
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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 and Introduction to Computational Mathematics |
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預期每週課後學習時數 |
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Office Hours |
每週三 16:00~17:00 |
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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)
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) |
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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 |
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 |
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週次 |
日期 |
單元主題 |
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第1週 |
09/08 |
course overview, linear algebra review |
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第2週 |
09/15 |
projectors, singular value decomposition, least squares problems
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第3週 |
09/22 |
QR factorization, conditioning of linear systems |
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第4週 |
09/29 |
conditioning of least squares problems |
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第8週 |
10/27 |
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第10週 |
11/10 |
Midterm
Time: 09:10-12:00
Topics: Week 1-8
Open books and notes |
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第11週 |
11/17 |
No class: Self-learning week
Term project proposal due |
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第16週 |
12/22 |
22:00, 12/23, Written term report due |
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