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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 |
112-1 |
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授課對象 |
理學院 數學研究所 |
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授課教師 |
王偉仲 |
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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 |
Course web site: https://sites.google.com/view/nla2023f/
Topics to be covered will include:
1. Orthogonality
2. Singular value decomposition (SVD)
3. QR factorization
4. Linear least-squares
5. LU and Cholesky Factorizations
6. Sparse Linear Systems
7. Conjugate Gradient Method
8. Eigenvalues and Eigenvectors
9. Arnodi Method
10. Computing SVD |
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課程目標 |
This course encompasses essential and cutting-edge concepts, algorithms, theories, and implementations in numerical linear algebra. Students will gain comprehensive insights and hands-on experience, exploring the subject from applications, mathematics, and computation perspectives. |
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課程要求 |
Linear Algebra, Calculus, Introduction to Computational Mathematics, Programming Language (e.g., Python, MATLAB, Julia, C, C++, or CUDA), Mathematical Analysis |
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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 |
"Advanced Linear Algebra: Foundations to Frontiers" by Robert van de Geijn, Margaret Myers, 2023. |
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參考書目 |
"Numerical Linear Algebra" by Lloyd N. Trefethen and David Bau III, SIAM
"Linear Algebra and Learning from Data" by Gilbert Strang, ISBN: 9780692196380, 2019
https://ocw.mit.edu/courses/mathematics/18-065-matrix-methods-in-data-analysis-signal-processing-and-machine-learning-spring-2018/index.htm
"Introduction to Applied Linear Algebra – Vectors, Matrices, and Least Squares" by Stephen Boyd and Lieven Vandenberghe (http://vmls-book.stanford.edu/)
"Mathematics for Machine Learning" by Marc Peter Deisenroth, A. Aldo Faisal, and Cheng Soon Ong, 2020 (https://mml-book.com)
"Linear Algebra for Everyone" by Gilbert Strang, ISBN 978-1-7331466-3-0, 2020
"Applied Numerical Linear Algebra" by James W. Demmel, SIAM, 1997
"Matrix Computations" by Gene H. Golub and Charles F. Van Loan, ISDN: 1421407949, Fourth Edition, 2013
"Iterative Methods for Sparse Linear Systems" by Yousef Saad, 2nd Edition, 2003 (http://www-users.cs.umn.edu/~saad/IterMethBook_2ndEd.pdf)
Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods, 2nd Edition, Richard Barrett et al., SIAM, 1994
大型線性系統與特徵值問題 http://ocw.lib.ntnu.edu.tw/course/view.php?id=190 |
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評量方式
(僅供參考) |
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