Syllabus: MTH 653, Spring 2017, Numerical Linear Algebra

Instructor:	Jay Gopalakrishnan
Times:	Tue, Thu: 12:00-13:15
Venue:	NH373
Office hours:	NH309, Thu 13:30-14:30

Learning Outcomes

Students will enhance their knowledge of basic algorithms in dense linear algebra, learn advanced techniques on iterative solution of large sparse linear and eigenvalue systems, and implement practical preconditioners.

Prerequisites

A solid undergraduate background in linear algebra is expected for this graduate course.

Topical outline

SVD. Orthogonalization. Householder reflections. Givens rotations. Least-squares. Further factorizations.

Large sparse matrices. Finite elements. Conditioning.

Conjugate gradients. Arnoldi iteration. Lanczos iteration. GMRES.

Preconditioning. Fictitious space lemma. Auxiliary space preconditioners.

Dense eigenvalue problems. QR iteration. Divide & Conquer algorithm.

Sparse eigenvalue problems. Subspace iterations. Advanced techniques.

Learning methods

In addition to lectures, students learn through hands-on programming sessions and problem solving sessions. Students will be required to present homework solutions to the entire class.

The programming language used in the course will be Python 3. If you are not familiar with it, please start with the good tutorial by the inventor of Python. Then procced to Scipy lectures.

To obtain finite element matrices and experiment with preconditioning and other advanced strategies, we will use the python interface to the open-source NGSolve package. Make sure you have it installed (there will be students in the class who can help with this install) and if you are new to it, start with this tutorial.

Textbook: Numerical linear algebra, by Lloyd N. Trefethen and David Bau III, published by SIAM, 1997. Many students have found this book to be useful and inspiring. However, please be aware that much of the learning material will not come from this book or from any single source.

Evaluation

Grades will be assigned based on performance in projects and an oral examination.

Fine print

Title IX Reporting Obligations: Every instructor at PSU has the responsibility to help create a safe learning environment for students and for the campus as a whole. Accordingly, the instructor must report any instances of sexual harassment, sexual violence and/or other forms of prohibited discrimination. If you would rather share information about sexual harassment, sexual violence or discrimination to a confidential employee who does not have this reporting responsibility, please use the online list of those individuals. For more information about Title IX please complete the student module Creating a Safe Campus in D2L.

Academic Misconduct: In the list of prohibited student behavior at PSU is plagiarism, buying and selling of course assignments, and obstruction of another student's success. Students are expected to know of and refrain from all proscribed conduct.

Disability Accommodations: The Disability Resource Center (DRC) provides reasonable accommodations for students who encounter barriers in the learning environment. If you have, or think you may have, a disability that may affect your work in this class and feel you need accommodations, contact the DRC to schedule an appointment and initiate a conversation about reasonable accommodations. The DRC is located in 116 Smith Memorial Student Union, 503-725-4150, drc@pdx.edu, https://www.pdx.edu/drc. Students who have testing accommodations must begin the test at the same time as the rest of the class.

Copyrighted Materials: All course materials handed out in class or placed in D2L are protected by copyright laws, and are for individual student's personal use only. Multiple copies or sale of these materials is prohibited.