Numerical Linear Algebra


Math 6643, Fall, 2007
Tuesdays and Thursdays, 1:35-2:55 p.m. in Skiles 256

Instructor: Haomin Zhou (email: hmzhou@math.gatech.edu)
Office Hours: Tue., Thur. 11:00a.m. - 12:00 p.m. or by appointment


Course Information


Reference Books :

  • Numerical Linear Algebra , by Lloyd N. Trefethen and David Bau, III, published by SIAM.
  • Iterative Methods for Solving Linear Systems , by Anne Greenbaum, published by SIAM.


    • Tentative Course Materials:

  • 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 and Singular Value Decomposition
  • 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 two term projects involving computer programming. Your grade will be based on the performance of the projects (50% each). Late submission will NOT be accepted unless for special reasons (you must show me the evidence).

    Homework will be assigned but will not be collected and graded. You are encouraged to discuss with classmates.

    The first project is available here .
    The second project is available here .