Numerical Linear Algebra


Math 6643, Spring, 2017
Monday 9:35-10:55 (Pink Room), Tuesdsay 6:05-7:35 (Pink Room)

Instructor: Wing Suet Li (email: li@math.gatech.edu)
Office Hours: M, 2:00 p.m. - 3:00pm, W, 9:00 - 10:00 or by appointment


Course Information


Reference Books :

  •  Numerical Linear Algebra , by Lloyd N. Trefethen and David Bau, III, published by SIAM.
  • Applied Numerical Linear Algebra , by James W. Demmel, published by SIAM.
  •  Iterative Methods for Sparse Linear Systems, by Yosef Saad, published by SIAM.
  •  Matrix Computations, by G. Golub and C. Van Loan, published by Johns Hopkins University.

    • 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.
  • Introduction to Multigrid.

    • Grading:

    There will be 6 homework assignments. The due dates for these homework sets are: Jan. 24, Feb. 7, Feb. 28, Mar. 21, Apr. 4, and Apr. 18. There will be one inclass midterm exam, on March 7. Final will be optional. Your grade will be based on the performance of the midterm exam and homeworks. Late submission will NOT be accepted unless for special reasons (you must show me the evidence).
    You can chosees one of the following to calculate your final grade:
  • 40% midterm, 6 x 10%=60% homework.
  • 20% midterm, 30% final, drop the lowest homework, 5 X 10% = 50% homework.
    • 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.

    Homework assignments will be upload on t-square.