Lectures:  MWF 11:05-11:55 am
Location:  MRDC 2404

Instructor:  Edmond Chow
E-mail:
Office Hours: Fridays 3-4 pm in KACB 1312

TA: Emily Rogers (emilyrogers@gatech.edu): Mon/Wed 1:30-2:30 in Skiles 016
TA: Kimis Perros (perros@gatech.edu): Tue/Thur 11:00-12:00 in KACB 1211
TA: Ruilin Li (ruilin.li@gatech.edu): Tue/Thur 10:00-11:00 in Skiles 146B

Course Description

Introduction to numerical solutions of the classical problems of linear algebra including linear systems, least squares, and eigenvalue problems.

Prerequisites

Undergraduate linear algebra (including eigenvalues and eigenvectors) taken relatively recently. The assignments will require Matlab programming (at least at the level of CS 1371). An undergraduate level course in numerical methods (e.g., MATH 4640) is strongly recommended.

Topics

• Singular value decomposition
• Least squares problems and QR factorization
• Conditioning and stability
• Direct methods for solving linear systems
• Eigenvalue problems and the QR algorithm
• Introduction to iterative methods

Learning Objectives

Students will develop facility with the methods of numerical linear algebra, e.g., various factorizations, iterative methods, and their analysis. This leads to the following larger learning objectives for students in this course. The students will be able to:

• Model a real-world problem as a problem in numerical linear algebra
• Select or design a method or approach for solving a problem in numerical linear algebra
• Evaulate a method for its accuracy, stability, and computational cost
• Discuss efficiency implications in a computer implementation of a method, including parallel computing aspects
• Use Matlab and other numerical software appropriately, i.e., understand when to use certain methods and their limitations

30% Assignments

30% Midterms: Wed Feb 1, Fri Feb 24, Wed Mar 29

40% Final exam: Fri Apr 28 at 8 am. Students must pass the final exam to pass the course.

Required Textbooks

• Numerical Linear Algebra, by Trefethen and Bau, SIAM, 1997. This is a very clearly written text, and we will cover the entire book. You can order this book from SIAM here. You can get a 30 percent discount if you are a SIAM member. As a student, you can join SIAM for free, since Georgia Tech is an Academic Member. Check it out here!
• Matrix Computations, 3rd edition, by Golub and van Loan, Johns Hopkins University Press, 1996. This is the bible of numerical linear algebra. Advanced material will be taken from this book. I recommend ordering this book from the Web from your choice of vendor.