MATH 639 -- 600 -- ITERATIVE TECHNIQUE, Spring 2004
General information
- Instructor: Dr. Raytcho Lazarov, Blocker 505C, 845 7578
- Time: TR 8:00 - 9:15 am
- Classroom: BLOC 120
- Labs (by Dukjin Nam):
Classroom: BLOC 126, Time: W 3:00 - 3:50 pm;
To visit the labs homepage click here
- Office Hours: TR 10:00 am -- 11:00 am or by appointment
- Text: (Required) Iterative Solution for Sparse Systems, by Y. Saad,
SIAM, 2003 and (Suggetsted) Iterative Solution of Large Sparse Systems
of Equations, by W. Hackbusch, Springer-Verlag, 1994.
- For freely available software for Linear Algebra on web
clik here
Course description
-
This is a one-semester course in the general area
of numerical analysis. Theoretical and computational aspects
to various classical and advanced iterative methods for
large systems of linear and nonlinear equations will
be discussed. Application of these methods
to systems arising from approximation of
differential equations will be the main object of the course.
- The prerequisites are one
semester of numerical linear algebra, one semester of
numerical analysis and some knowledge of
a programming language.
Course Outline
- Recapitulation of Linear Algebra: vector and matrix norms,
correlation between norms and the spectral raduis, positive definite matrices
- Iterative methods - general concepts: fixed points,
consistency and convergence,
linear iterative methods, convergence speed, Gauss-Seidel, Jacobi,
SOR, SSOR, Richardson methods, the concept of preconditioning
- Conjugate gradient methods (variational methods or Krylov subspace):
minimization problem and search directions, gradient method,
method of conjugate directions, conjugate gradient method (CG),
methods of conjugate residuals, method of minimal residuals;
preconditioning and preconditioned methods (of the types described above)
- Newton and quasi-Newton methods for nonlinear systems
Grading Policy
- Your grade for the course will be computed as follows:
- your MINIMUM grade will be A, B, C, or D, for averages of
90%, 80%, 65%, or 50%, respectively.