数值代数
学分：3学分
先修课程：实分析与微积分；向量、几何与线性代数；多元微积分与向量分析
课程简介和目标：
数值代数为暨南大学信息与计算科学专业本科生的专业必修课，它也适用于需要学习数值方法的各理工科专业的学生。先修课程包括线性代数和MATLAB编程语言。课程共计72学时，包括36学时的理论课和36学时的实验课。
课程内容主要包括：线性方程组的求解算法，例如适用于一般方程组的Guass消元法、列主元Guass消元法、适用于线性方程组中的最小二乘问题的正则化和正交化方法，以及适用于稀疏方程组的古典迭代法、共轭梯度法；特征值特征向量问题的求解算法，例如幂法、反幂法和QR方法等；除了介绍算法以外，课程还会涉及一些对问题和算法进行一些理论分析的内容。
通过本课程的学习，可以使学生掌握线性代数问题的主流数值求解算法，并且能够自己编程实现，用以求解以后的学习和研究中碰到的线性代数问题。本课程也会对学生将来为新的数学问题设计算法、分析算法提供启发。
成绩评定方式：
评定：学期总评成绩（100％）
重评：补考卷面成绩（100％）
成绩评定要求出勤率
推荐教材：
徐树方等编著，数值线性代数（第二版），北京大学出版社，2013.01。
Numerical Algebra
Credits: 3 Credits
Pre-requisite: Real Analysis & the Calculus; Vectors, Geometry & Linear Algebra; Multivariable & Vector Analysis
Description：
Numerical linear algebra is a compulsory course for undergraduates major in Information and Computing Science, it also can be taken as an elective course for the students who want to study numerical methods. One should have studied Linear algebra and Matlab before taking this course. It contains 72 classes, including 36 theory classes and 36 experimental classes.
The main content of this course is as follows: 1. Numerical algorithms for linear systems, including some direct methods for general linear systems, the orthogonal method for least squares problem, and some standard iterative methods and the conjugate gradient method for the sparse linear systems. 2. Numerical algorithms for eigenvalue problem, including the power method, the inverse power method and the QR method. 3. Theory analysis of the problems and the algorithms.
By taking this course, students can learn the most important numerical methods for linear algebra problems, and can program these methods by themselves. They are expected to have the ability to numerically solve the linear problems arisen in their future study and research.
Methods of Summative Assessment：
Assessment: Assessments done during semester (100%)
Reassessment: best of 3 hour resit examination (100%)
Attendance at tutorials is a required element of this module.
Recommended textbooks：
Xu Shufang, Numerical Algebra, 2nd Edition, Peking University Press, 2013.01.
Detailed Lecture Notes will be provided to students.
