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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 |
104-1 |
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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 |
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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 |
星期二7,8(14:20~16:20)星期四7,8(14:20~16:20) |
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上課地點 |
天數430天數430 |
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備註 |
總人數上限：13人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1041nla |
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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 |
如果你坐過高鐵，用過 google，點過手機裡的廣告，tag 過相片，或是看過阿凡達，那麼你已經體驗過數值線性代數軟體的威力。結合數學與電腦的「數值線性代數」和「計算與資料科學軟體開發」兩門課程，協助你掌握當今科學、工程、科技、資料分析的核心工具，成為各種先進應用研發的要角。「數值線性代數」(https://goo.gl/nCP4cz) 與「計算與資料科學軟體開發」(https://goo.gl/TkZQOB)，前者種理論，後者重實作，讓你在數據化的現代社會中更出色！
This course covers basic and state-of-the-art concepts, algorithms, theories, and implementations in numerical linear algebra. Students will learn and practice the subjects from the viewpoints of application, mathematics, and computing. We plan to cover the following topics.
- Fundamentals (four subspaces, matrix-vector multiplication, orthogonal vector, norms, projection, sparse matrix, conditioning, stability)
- Linear systems (Gaussian elimination, pivoting, Cholesky decomposition, stationary iterative methods, Krylov subspace methods)
- Eigenvalue problems (Reduction to Hessenberg and tridiagonal form, Rayleigh quotient and inverse iteration, QR, Jacobi-Davidson, Shift-and-Invert Residual, Arnoldi, contour integral
- Singular value decomposition
- Least square problems (normal equations, QR decomposition, Gram-Schmidt orthogonalization, Householder transformations, Givens rotation)
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課程目標 |
The goals of this course are (i) to provide theoretical insight and computational hands-on experience in numerical linear algebra and (ii) to guide students to conduct researches in selected topics. With the training of the course, we expect the students can choose efficient algorithms and software to solve their problems and have enough backgrounds to develop new methods and tools.
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課程要求 |
Linear Algebra, Programming Language (e.g. MATLAB, C, C++, and/or CUDA), Introduction to Computational Mathematics, Calculus |
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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 |
L. N. Trefethen and D. Bau, III, Numerical Linear Algebra, SIAM 1997. (e-book) |
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參考書目 |
- Applied Numerical Linear Algebra, James W. Demmel, SIAM, 1997
- Iterative Methods for Sparse Linear Systems, 2nd Edition, Yousef Saad, 2003 (http://www-users.cs.umn.edu/~saad/IterMethBook_2ndEd.pdf)
- Matrix Computations, Fourth Edition, Gene H. Golub and Charles F. Van Loan, SIAM, 2013
- Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods, 2nd Edition, Richard Barrett et al., SIAM, 1994
- G. Allaire and S. M. Kaber, Numerical Linear Algebra, Springer 2008. (e-book)
- A. Greenbaum, Iterative Methods for Solving Linear Systems, SIAM 1997.
- H. A. van der Vorst, Iterative Methods for Large Linear Systems, 2002. (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. |
課堂討論，課堂報告，上課表現 |
20% |
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2. |
期中考 |
40% |
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3. |
期末考 |
40% |
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