課程資訊
課程名稱
數值線性代數
Numerical Linear Algebra 
開課學期
101-1 
授課對象
理學院  數學系  
授課教師
薛克民 
課號
MATH5411 
課程識別碼
221 U4210 
班次
 
學分
全/半年
半年 
必/選修
選修 
上課時間
星期一@,7,8(~16:20) 
上課地點
天數305 
備註
總人數上限:30人 
Ceiba 課程網頁
http://ceiba.ntu.edu.tw/1011nla 
課程簡介影片
 
核心能力關聯
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課程大綱
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課程概述

This is an introductory graduate level course on numerical linear algebra.
Topics to be covered will include:

1. Review of relevant linear algebra
(a) Vector and matrix norms
(b) Orthogonality
(c) Spectral theory of matrices

2. Direct methods for linear systems
(a) Perturbation theory
(b) Gaussian elimination
(c) Stability of Gaussian elimination
(d) Cholesky method
(e) QR factorization method

3. Least square problems
(a) Normal equation method
(b) QR factorization method
(c) Householder algorithm
(d) Conditioning of least square problems
(e) Stability of least square algorithms

4. Iterative methods for linear systems
(a) Jacobi, Gauss-Seidel, and relaxation methods
(b) Steepest descent methods
(c) Conjugate gradient method
(d) variant Krylov subspace methods

5. Nonsymmetric eigenvalue problems
(a) Power method
(b) Inverse iteration
(c) Orthogonal iteration
(d) QR iteration

6. Symmetric eigenvalue problems
(a) Tri-diagonal QR iteration
(b) Rayleigh quotient iteration
(c) Bisection and inverse iteration
(d) Jacobi's method

7. Singular value decomposition
(a) QR iteration
(b) Jacobi's method
(c) Application to rank-deficient least square problems

Continuation of this course to next semester will be on numerical optimization. 

課程目標
The goal of this course is to provide theoretical insight and to
develop practical skills for solving large scale linear algebra problems
numerically. 
課程要求
先修課程: Linear Algebra & Introduction to Computational Mathematics 
預期每週課後學習時數
 
Office Hours
每週三 11:00~12:00 
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, The Johns Hopkins
University Press, Baltimore, 3rd ed., 1996.
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. W.-W. Lin, Lecture notes of matrix computations, 2010. (e-lecture) 
指定閱讀
 
評量方式
(僅供參考)
 
No.
項目
百分比
說明
1. 
Final 
40% 
 
2. 
Homework 
60% 
 
 
課程進度
週次
日期
單元主題
第1週
9/10,9/12  Fundamentals of matrix analysis 
第2週
9/17,9/19  vector space & norms 
第3週
9/24,9/26  LU & error analysis  
第4週
10/01,10/03  PLU & Cholesky factorization 
第5週
10/08,10/10  Least-squares problems 
第6週
10/15,10/17  Householder triangularization 
第7週
10/22,10/24  Gram-Schmidt's method &
Conditioning of least-square problems 
第8週
10/29,10/31  Updating QR & basic iterative method 
第9週
11/05,11/07  Conjugate gradient method