Numerical Linear Algebra

CSE/Math 6643, Spring, 2018
Monday, Wednesday 2:00pm - 3:50pm (A 402)

Instructor: Wing Suet Li (email: li@math.gatech.edu)
Office Hours: M, W 11:00 a.m. - 12:00pm, or by appointment

Course Information

Text Books :

•  Numerical Linear Algebra , by Lloyd N. Trefethen and David Bau, III, published by SIAM.
• Topics covered:

Introduction:
• Fundamentals including vector, matrix, norms, eigenvalues, singular values.
• Linear systems, least square problems.
• QR factorization. Gram-Schmidt process, Householder transformation.
• Stability and conditioning.
• Direct methods for solving linear systems:
• Gaussian Elimination, pivoting.
• LU, Cholesky factorizations, .
• Eigenvalues, Singular Value Decomposition, and Least Square Problems
• Rayleigh Quotient, Inverse Iteration.
• QR algorithm.
• Divide-and-Conquer algorithm.
• SVD.
• Iterative methods for solving linear systems
• Gauss-Jacobi, Gauss-Seidel, SOR.
• Krylov subspace methods, Conjugate Gradients, GMRES.

There will be 4 homework assignments. The due dates for these homework sets are: January. 24, February. 7, February. 28, March. 7, and March 21. The inclass Midterm exam is schedule for February 12 and the Final is for March 26. Due to the compact on-sight schedule, a final project will be assigned and the due date is May 1st.

Your grade will be based on the performance of the homeworks, exams, and the final project. Late submission will NOT be accepted unless for special reasons (you must show me the evidence).

The final grade will be calculated according to the following:

• 4 x 10% = 40% homework
• Project 20%
• Midterm exam, 20%
• Final exam, 20%
• Curving will be done on the final result. You are guaranteed an A if 85% and above, B if 70%-84%, C if below %69.

The Honor Code and Academic Dishonesty:

• Do not cheat! Abide by the honor code at all times. See hornor code and Georgia Tech policy on academic misconduct here.

• Any evidence of cheating or other violations of the Georgia Tech Honor Code will be submitted directly to the Dean of Students. Cheating includes, but is not limited to:
• 1. Using a calculator, books, or any form of notes on quizzes or tests.
• 2. Copying directly from any source, including friends, classmates, tutors, internet sources
• 3. Allowing another person to copy your work.
• 4. Taking a test or quiz in someone else’s name, or having someone else take a test or quiz in your name.
• 5. Asking for a regrade of a paper that has been altered from its original form.