Instructor: Zhiyan Ding (zyding at umich.edu)
Class hours: Tu/Thur at 8:30am-10:00am at East Hall 1084.
Office hours: Tu/Thur at 10:00am-11:00am at East Hall 3830.
Course description:
The main topics of this class are the numerical solution of linear systems, the computation of eigenvalues and singular values, and the solution of linear least squares problems. We will discuss condition numbers, numerical stability, QR factorization, SVD, the QR algorithm as well as iterative methods (GMRES, Arnoldi, Conjugate Gradients, Lanczos). The following applications are included: KKT conditions, convergence of the perceptron, and back propagation networks. The homework assignments will use either Python or Matlab, with the choice left to the student.
Note: Lecture will be recorded. In most of the lecture, I will use slides, which will be uploaded after the class.
Textbook:
1. (Main) L.N. Trefethen and D. Bau III, Numerical Linear Algebra, SIAM.
Many of the lectures will draw from the following sources:
NJ Higham: Accuracy and Stability of Numerical Algorithms
Golub and van Loan: Matrix Computations
David S. Watkins: Fundamentals of Matrix Computations
A. Greenbaum: Iterative Methods for Solving Linear Systems
Prerequisite:
Math 214, 217, 417, 419, or 420 and one of Math 450, 451, or 454, or permission from the instructor.
Homework:
Homework will be assigned every week, and solutions will be posted at the same time.
You do not need to submit your homework—welcome to the AI age! However, you are expected to work through and understand the homework problems, since they will help prepare you for the quizzes.
Quiz:
There will be one quiz every week during the class, except during the first week.
Each quiz will consist of one problem and you will have 10 minutes to complete it. The quiz problem will always be very similar to one of the homework problems.
Each quiz will be graded out of 10 points. Your lowest quiz score will be dropped.
Evaluation:
There will be two exams for this class, one midterm and one final. In addition, there will be quiz every week, starting from the second week.
30% Quiz + 30% Midterm + 40% Final.
Attendance rule:
Because of the weekly quizzes, attendance is required for this class. Of course, I understand that there may be occasions when you need to miss class. Absences may be accommodated on a case-by-case basis, but you should let me know in advance and explain the reason so that we can arrange an appropriate way to make up the missed quiz.