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.