Iterative Methods for Systems of Equations


Math 6644, Spring, 2007
Tuesdays & Thursdays, 1:35-2:55 p.m. in Skiles 256

Instructor: Haomin Zhou (email: hmzhou@math.gatech.edu)
Office Hours: Tuesdays & Thursdays 10:30-11:30 a.m. or by appointment


Course Information


Reference Books:

  • Iterative Methods for Solving Linear Systems , by Anne Greenbaum, published by SIAM.
  • Iterative Methods for Linear and Nonlinear Equations, by C. T. Kelley, published by SIAM.


    • Tentative Course Materials:

  • Iterative Methods for Linear Systems:
  • Classical iterative methods: Gauss-Jacobi, Gauss-Seidel, SOR, SSOR.
  • Discreitzation of differential equations, and sparse matrices.
  • Krylov Subspace methods: Lanczos, CG, GMRES, MINRES, BiCG.
  • Preconditioning: Multigrid, Domain Decomposition.
  • Recent developments in the fields.
  • Iterative Methods for Nonlinear Systems:
  • Fixed point iteration.
  • Newton's methods.
  • Inexact Newton's methods.
  • Globally convergent methods.

    • Grading:

    There will be two term projects involving computer programming (and possibly 5-10 minutes presentations). One is due around midterm and one is due at the end of the semester. Your grade will be based on the performance of the term projects (50% each).

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

    The first project can be downloaded here.
    The second project can be downloaded here.