计算方法 Numerical method (Spring 2024)

计算方法
Numerical method

Instructor
刘景铖
Email	liu [at] nju [dot] edu [dot] cn
Office	计算机系 516
Class
Class meetings	周三 14:00-16:00 仙 Ⅱ-303
Textbooks
Timothy Sauer 数值分析 （Numerical Analysis）（原书第2版）. 机械工业出版社.
Teaching Assistants
傅心语，于逸潇
Email	{xyfu, yixiaoyu} [at] smail [dot] nju [dot] edu [dot] cn
Office	计算机系 410

Announcement

• Welcome

Course info

• Instructor: 刘景铖 ( liu [at] nju [dot] edu [dot] cn )

• Teaching assistants: 傅心语，于逸潇
• TA email: {xyfu, yixiaoyu} [at] smail [dot] nju [dot] edu [dot] cn
• Homework email: nm_nju_2024@163.com
• Class meeting:周三 14:00-16:00， 仙 Ⅱ-303
• Office hour: 周二 16:00-18:00?, 计算机系516 (subject to change)
• QQ群: 855212527.(加入时需报姓名、专业、学号)

Textbooks and Readings

• 数值分析 （Numerical Analysis）（原书第2版）. Timothy Sauer. 机械工业出版社.
• Numerical Algorithms: Methods for Computer Vision, Machine Learning, and Graphics. Justin Solomon. CRC Press
• Lx=b, Laplacian Solver and Their Algorithmic Applications. Nisheeth K. Vishnoi.

如果在获取教材方面有困难可以联系助教。(仅限英文版)

Collaboration on Homework

You are welcome to work on homework problems in study groups of no more than 3 people; however, you must always write up the solutions on your own, listing all collaborators at the top. Similarly, you may use books or online resources to help solve homework problems, but you must always credit all such sources in your writeup and you must never copy material verbatim.

We believe that most students can distinguish between helping other students and cheating. You may discuss approaches but your solution must be written by you and you only. You should acknowledge everyone whom you have worked with or who has given you any significant ideas about the homework.

Further, it is your responsibility to ensure that your solutions will not be visible to other students. If you use Github or another source control system to store your solutions electronically, you must ensure your account is configured so your solutions are not publicly visible. Many popular version control systems provide free repositories to students.

As a final note, we’d like to point out that collaboration on homework, while permitted, can be detrimental to your learning if misused. In particular, avoid collaborations where you do not contribute enough to your own satisfaction. Such a collaboration not only cheats you out of an opportunity to learn through homework, but can also affect your confidence. If you feel that you are not contributing enough to your group, then try to spend time thinking about the problems alone before working with your group. If you end up solving the problem all by yourself, that’s great! And if not, you’ll still be better prepared to contribute to your group.

See also ACM Policy on Plagiarism.

Assignments

Late policy: In general, we will accomodate late submission requests ONLY IF you made such requests ahead of time.

1. Homework1 请在 2024年03月12日23点59分之前提交到 nm_nju_2024@163.com (文件名为'学号_姓名_A1.pdf') Homework1 提交名单
2. Homework2 请在 2024年03月26日23点59分之前提交到 nm_nju_2024@163.com (文件名为'学号_姓名_A2.pdf') Homework2 提交名单
3. Homework3 请在 2024年04月09日23点59分之前提交到 nm_nju_2024@163.com (文件名为'学号_姓名_A3.pdf') Homework3 提交名单
4. Homework4 请在 2024年05月01日23点59分之前提交到 nm_nju_2024@163.com (文件名为'学号_姓名_A4.pdf') Homework4 提交名单
5. Homework5 请在 2024年05月14日23点59分之前提交到 nm_nju_2024@163.com (文件名为'学号_姓名_A5.pdf') Homework5 提交名单
6. Homework6 请在 2024年05月28日23点59分之前提交到 nm_nju_2024@163.com (文件名为'学号_姓名_A6.pdf') Homework6 提交名单
7. Homework7 请在 2024年06月11日23点59分之前提交到 nm_nju_2024@163.com (文件名为'学号_姓名_A7.pdf') Homework7 提交名单

Lecture Notes

如果有下载课件的问题请及时联系助教。

1. 课程简介，函数求根
2. 牛顿法，插值，秘密分享，自纠错码
3. Chebyshev插值与多项式，范数
4. 最小二乘法，Gram-Schmidt正交化与QR分解
5. FFT，高斯消元与LU分解
6. 算子范数，条件数和迭代法
7. 特征值与幂迭代
8. 特征值的其它迭代方法与SVD
   • Further reading: lecture note by Tim Roughgarden and Greg Valiant on matrix completions
9. 迭代法解线性方程组：梯度下降方法与共轭梯度
10. 幂迭代的特例：随机游走与马尔可夫链
11. 谱图论
12. 电阻电路网络
13. 碰撞时间、遍历时间和线性规划入门
14. 对偶性原理与应用
15. 强对偶性、课程回顾