Lectures:  Tuesdays and Thursdays 12:30-1:45
Location:  MRDC 2404

Instructor:  Edmond Chow
E-mail: 

TA: Rafael Orozco (rorozco@gatech.edu)
TA: Sooyoun Oh (soh342@gatech.edu)
TA: Yuening Tang (ytang322@gatech.edu)


Course Description

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

Prerequisites

A four-credit or two-semester course in linear algebra, equivalent to MATH 1554 (subspaces, rank, Gram-Schmidt, QR, least squares, eigenvalues, eigenvectors, singular value decomposition, vector norms). 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

Grading

35% Assignments

10% Final exam

10% Weekly journaling

30% Student tutorials

15% Participation

Required Textbooks

  • Numerical Linear Algebra, by Trefethen and Bau, SIAM, 1997. 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 by Golub and van Loan. Any edition.