课程大纲
COURSE SYLLABUS
1.
课程代码/名称
Course Code/Title
MAT7081 矩阵计算 Matrix Computations
2.
课程性质
Compulsory/Elective
选修
/Elective
3.
课程学分/学时
Course Credit/Hours
3/48
4.
授课语言
Teaching Language
中英文， Chinese & English
5.
授课教师
Instructor(s)
杨将副教授、Alexander Kurganov 教授
Jiang Yang, Associate Professor；Alexander Kurganov，Professor
6.
是否面向本科生开放
Open to undergraduates
or not
否/No
7.
先修要求
Pre-requisites
MA103b 203b 线性代数 I&II, MA305 数值分析
Linear Algebra I &II, MA305 Numerical Analysis
8.
教学目标
Course Objectives
Matrix is the key mathematical tool for describing the problems in science, engineering, economics, and
industry. This course is for students interested in understanding or further developing stable and
efficient algorithms for systems of linear equations, least squares problems, eigenvalue problems,
singular value problems and some of their generalizations and applications. In this course, techniques
for dense and sparse, structured problems, parallel techniques and direct and iterative methods will be
covered. Students will come to appreciate many state-of –the –art algorithms or matrix methods, and
will have the ability to quantify and analyze many practical applications and be far easier to deal with
them by applying the matrix methods.
9.
教学方法
Teaching Methods
By presenting the motivating ideas for each algorithm, we try to stimulate the students intuition and
make the technical details easier to follow.
10.
教学内容
Course Contents
（如面向本科生开放，请注明区分内容。 If the course is open to undergraduates, please indicate the
difference.）
Section 1
Matrix Multiplication Problems 6 Hours
Section 2
Matrix Analysis 4 Hours
Section 3
General Linear Systems 5 Hours
Section 4
Special Linear Systems 9 Hours
Section 5
Orthogonalization and Least Squares 8 Hours
Section 6
Parallel Matrix Computations 4 Hours
Section 7
The Unsymmetric Eigenvalue Problem 9 Hours
Section 8
The Symmetric Eigenvalue Problem 9 Hours
Section 9
Lanczos Methods 4 Hours
Section 10
Iterative Methods for Linear Systems 6 Hours
Section 11
Functions of Matrices 3 Hours
11.
课程考核
Course Assessment
Exercise (20%),
Quiz+Projects (30%)
examination (50%)
12.
教材及其它参考资料
Textbook and Supplementary Readings
Textbook:
Gene H. Golub, Charles F. Van Loan, Matrix Computations, 3rd Edition, The John Hopkins University
Press, Baltimore and London, 1996.
Supplementary Readings:
1. Gibert Strang, Introduction to Linear Algebra, 4th Edition, Wellesley-Cambridge and SIAM, 2009.
2. Carl D. Meyer ,Matrix Analysis and Applied Linear Algebra, SIAM.
3. David Watkins, Fundamentals of Matrix Computations, Wiley, 1991.
