## Numerical Linear Algebra, CMSE 823

 Instructor: Mark Iwen Time and Place: Lectures are Tu Th 8:30 am -- 9:50 am, in B104 Wells Hall E-mail: markiwen@math.msu.edu Office: C342 WH Office Hours: Tu 10:00 am -- 11:00 am, and Th 10:00 am -- 11:00 am

This course will cover numerical methods for efficiently solving linear equations and eigenvalue problems. Emphasis will be on the design and analysis of efficient and stable numerical schemes. Students will learn how to solve least squares problems, how to numerically approximate eigenvalues/eigenvectors of matrices, how to compute fundamental matrix factorizations (LDU, SVD, QR, Cholesky, ...), and how to determine the best numerical method to use for doing all of these based on the characteristics of a given linear system (repeated eigenvalues, ill-conditioned systems, etc.). In order to understand why specific methods will or won't work in specific settings, we'll also need some basic knowledge of matrix analysis (e.g., matrix norms, condition numbers, basic perturbation theory).

#### Course website for CMSE 823-001:

http://math.msu.edu/~markiwen/Teaching/CMSE823/CMSE823_F16.html

The course website is mandatory reading for the course. On it you will find the course schedule, the syllabus, and supplementary reading. Homework assignments will be posted on the schedule.

#### Textbook:

Numerical Linear Algebra, by Lloyd N. Trefethen and David Bau III.
SIAM, 1997.

The majority of the course will be spent covering this book from cover to cover.

#### Supplementary Texts:

We will also utilize material from the following books, all of which are highly recommended (but not required):

• Applied Numerical Linear Algebra, by James W. Demmel.
SIAM, 1997.
• Matrix Analysis (2nd edition), by Roger A. Horn and Charles R. Johnson.
Cambridge University Press, 2013.
• Matrix Perturbation Theory, by G. W. Stewart and Ji-guang Sun.

#### Homework:

Homework assignments will be given every week and will constitute 10% of your final grade. The homework questions will be posted on the web with their due dates. Posting of new assignments will be announced in class. You must submit your homework solutions during the class period on the due date unless prior permission has been granted to submit otherwise. Late homework assignments will never be graded. The lowest homework score will be dropped when computing your average homework grade. Homework solutions must be original copies in the student's own handwriting. No other submissions will be graded. Solutions must be clear and neatly written to receive credit. A subset of the homework problems will be graded each week.

#### Exams:

You will be given two in-class midterm exams, and one cumulative final exam. The midterm exams will count 50% toward your final grade. The cumulative final exam will count 40% toward your final grade. There are no make-up exams, ever. A student who finds it necessary to miss an exam should contact the professor before the exam to explain the circumstances. If an exam is missed due to an excused medical emergency, or for any other excused reason, then the student's grade on the cumulative final exam will substitute their missed midterm exam score.

You will be given the first in-class midterm exam during class on Thursday, September 29th. The second in-class midterm exam will be given during class on Thursday, November 3rd. The cumulative final exam will be held on Monday, December 12th, from 7:45am - 9:45am.

Your final course percentage will be determined by averaging your homework, midterm exam, and final exam percentages with the following weights: Homework (10%), Midterm Exams (50%), and the Final Exam (40%). The result of this weighted average will then be rounded to the nearest integer.

Your final grade (e.g., 3.5, 4.0, etc.) will be assigned according to a class ranking. That is, the weighted averages calculated as above for all the students in the class will be rank ordered. Finally, threshold scores (e.g., a score above which a 4.0 is earned) will be determined, thereby establishing each student's final grade in the class. The threshold scores for each grade will never be higher than those indicated in following table.

 90% -- 100% A 4 85% -- 89% A-/B+ 3.5 80% -- 84% B 3 75% -- 79% B-/C+ 2.5 70% -- 74% C 2 65% -- 69% C-/D+ 1.5 60% -- 64% D 1 0% -- 59% F 0

This is a qualifier course for CMSE. Only a score of 3.5 or above will provide you with the subject competency you need in order to pass this qualification requirement. Study!

Incomplete grades will be given only in unusual cases of illness or other personal emergency, which causes the student to miss a significant amount of the course. This grade cannot be given for any other reason.