MTH 451- 551 : NUMERICAL LINEAR ALGEBRA - Fall 2017
General information
Assignments
General information
Instructor: Malgorzata Peszynska (Contact information including office hours is on Instructor's website. See also department website )
Class: MWF 10:00-10:50 STAG 262. Credits:3.
Prerequisites: Solid skills in real variables, and linear algebra (MTH 341) are the prerequisites; MTH 342 and MTH 351 are recommended. Prior computing experience is not required but students will be expected to grow in their computational and theoretical abilities.
Numerical Linear Algebra is the foundation of Computational and Data Science; it provides the basis (no pun intended) for the modern machine and deep learning, imaging science, optimization, and the solution of large (non)linear systems of equations arising in various applications. In this class you will learn the basic concepts, algorithms, and you will have a chance to sample some of the applications.
Course content:
1. Numerical solution of linear systems using direct and iterative methods, factorizations and decomposition of matrices.
2. Stability and accuracy of numerical methods for linear algebra.
3. Orthogonal decompositions, SVD (singular value decomposition) and least squares, as used in imaging, optimization, and other applications.
4. Numerical methods for finding eigenvalues and eigenvectors.
5. Iterative methods for solving large linear systems, with emphasis on the positive definite systems.

Exams: There will be two exams: a midterm (in class) on Friday October 20, and a Final Exam on Tuesday, Dec 5, at 0930. Each exam will count as 30% of the grade.
Homework and quizzes: Homework will count as 30% of the grade and will be assigned (almost always) weekly. The two lowest scores of HW1...HW6, or HW 7 (counted double), will be dropped.
There will also be weekly quizzes (usually on Fridays) which will count together as 10% of the grade. The quizzes will be based on the material announced in class before the quiz.
Course Learning Outcomes:
A successful student who completed MTH 451 will be able to
• Apply the basic direct and iterative methods for solving linear systems
• Implement and justify convergence of model iterative methods for solving linear systems
• Follow analyses of stability and accuracy of an algorithm, and determine accuracy experimentally
• Propose an appropriate method for a given linear system and a desired decomposition of a given matrix
A successful student who completed MTH 551 will be able to
• Analyze, select and test selected direct and iterative methods for solving linear systems
• Implement and analyze convergence of selected iterative methods for solving linear systems
• Carry out analyses of stability and accuracy of an algorithm, and determine accuracy experimentally
• Propose an appropriate method for solving a linear system or for decomposition of a matrix of particular type.
• Carry out demonstrations of applicability of the selected numerical linear algebra methods.

 Textbook: NUMERICAL LINEAR ALGEBRA Lloyd N. Trefethen and David Bau, III xii+361 pages; SIAM, 1997 Softcover / ISBN-13: 978-0-898713-61-9 / ISBN-10: 0-89871-361-7 / MATLAB: there exist plenty of good resources for MATLAB, some available online (search, for example, for "matlab tutorial free").

Statement Regarding Students with Disabilities: Accommodations for students with disabilities are determined and approved by Disability Access Services (DAS). If you, as a student, believe you are eligible for accommodations but have not obtained approval please contact DAS immediately at 541-737-4098 or at http://ds.oregonstate.edu. DAS notifies students and faculty members of approved academic accommodations and coordinates implementation of those accommodations. While not required, students and faculty members are encouraged to discuss details of the implementation of individual accommodations. The DAS Statement is posted online at: ds.oregonstate.edu/faculty-advisors (4/14/16).
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