# Fall 2018

## Course Information

Meeting times and room: Tu + Th 2:15-3:55 in MSB 158

Instructor: Lothar Reichel
Office: MSB 366
Office hours: Tu + Th 4-5:30 and by appointment
E-mail: reichel@math.kent.edu (Please use this e-mail address!)
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.
The desired learning outcomes are described here.
Class operation
Homework will be assigned regularly and collected at the end of each major section. Homework problems can be found here.
There will be a mid-term exam and a final exam. The final exam is on Tuesday December 13, 12:45-3:00 p.m.