Course Information

Meeting times and room: Mo + We 2:15-3:55 in MSB 376.
The class will be in person. In the unfortunate event that your instructor
would get covid, the class may be online for a few days.

Instructor: Lothar Reichel
Office: MSB 366
Office hours: Mo 4:15-6:15, We 4:15-5:15, and by appointment
E-mail: reichel@math.kent.edu (Please use this e-mail address!)
Office phone: 330-672-9114

Course objective
The course focuses on Numerical Linear Algebra, which is fundamental for most areas of Scientific Computing. Many ideas and concept of importance in applied mathematics and computation will be discussed. These include several matrix factorization methods, such as QR and LU factorizations, as well as the singular value decomposition. The sensitivity of the computed results to errors in the data, as well as to round-off errors introduced during the computations, will be discussed. It is the purpose of this course to introduce state-of-the-art numerical methods and provide an understanding of their performance through analysis and application. The programming languages MATLAB and GNU Octave will be taught. Octave is similar to MATLAB and is available for free. The performance and properties of the numerical methods discussed will be illustrated using MATLAB. All students should get accounts on the Math/CS Network on which MATLAB is available. GNU Octave is a public domain language very similar to MATLAB, and can be used for homework assignments. Instructions on how to install GNU Octave on your PC are available here. A very basic MATLAB primer, which helps you get started if you do not know MATLAB can be found here.

Textbook
L. N. Trefethen and D. Bau, ``Numerical Linear Algebra'', SIAM, Philadelphia, 1997. Contact the instructor before ordering the book. It might save you money.

Prerequisite
Introduction to Numerical Computing I+II or similar courses. Contact instructor if you would like to take the course, but do not have any experience in scientific computing.

Course content

• Vector norms, orthogonal vectors and matrices, orthogonal projections.
• Matrix factorizations: QR factorization, the singular value decomposition, and LU factorization.
• Least-squares problems.
• Sensitivity to errors: Conditioning and stability.
• Eigenvalue and eigenvector computation.
• Introduction to iterative methods: the Arnoldi and Lanczos processes.

Class operation
Homework will be assigned regularly and collected at the end of each major section. Homework problems can be found here.

Grading policy
Homework and numerical experiments contribute 20%, the midterm and final exams contribute 40% each towards your course grade.

Registration
The official registration deadline for this course is 8/31/22. University policy requires all students to be officially registered in each class they are attending. Students who are not officially registered for a course by the published deadlines should not be attending classes and will not receive credit or a grade for the course. Each student must confirm enrollment by checking his/her class schedule (using Student Tools in FlashLine) prior to the deadline indicated. Registration errors must be corrected prior to the deadline.

Attendance
Attendence requirements are described here.

Plagiarism,
i.e., presenting someone else's work as your own is discussed here. This includes finding the answer of a homework problem in a book or in someone else's assignment, and copying it. Plagiarism, of course, is unacceptable.

Students with disabilities
University policy requires that students with disabilities be provided reasonable accommodations to ensure their equal access to course content. If you have a documented disability and require accommodations, then please contact the instructor at the beginning of the semester to make arrangements for necessary classroom adjustments. Please note, you must first verify your eligibility for these through Student Accessibility Services (contact 330-672-3391 or visit www.kent.edu/sas for more information on registration procedures).

Diversity statement
Kent State University is committed to the creation and maintenance of equitable and inclusive learning spaces. This course is a learning environment where all will be treated with respect and dignity, and where all individuals will have an equitable opportunity to succeed. The diversity that each student brings to this course is viewed as a strength and a benefit. Dimensions of diversity and their intersections include but are not limited to: race, ethnicity, national origin, primary language, age, gender identity and expression, sexual orientation, religious affiliation, mental and physical abilities, socio-economic status, family/caregiver status, and veteran status.