Iterative Methods for Systems of Equations

Department: 
MATH
Course Number: 
6644
Hours - Lecture: 
3
Hours - Lab: 
0
Hours - Recitation: 
0
Hours - Total Credit: 
3
Typical Scheduling: 
Every spring (MATH) and fall (CSE)

Iterative methods for linear and nonlinear systems of equations including Jacobi, G-S, SOR, CG, multigrid, fixed point methods, Newton quasi-Newton, updating, gradient methods. Crosslisted with CSE 6644.

Prerequisites: 

MATH 2406 or MATH 4305 or consent of School

Course Text: 

No text

Topic Outline: 
  • Review of Iterative Methods for Linear Systems - Gauss-Jacobi, Gauss-Seidel, SOR, convergence, implementation storage of sparse matrices, discretization of elliptic problems
  • Modern Iterative Methods for Linear Systems - Krylov subspace methods: conjugate gradient, GMRES, QMR, multigrid methods, domain decomposition, preconditioning
  • Nonlinear Problems - Unconstrained optimization, differential equations, bifurcation problems
  • Review of Fixed Point Methods - Fixed point iteration, convergence
  • Newton's Method - Local convergence, Kantorovich theory, implementation, termination, inexact Newton's methods
  • Globally Convergent Methods - Quasi-Newton methods, line searches, model-trust region approach, convergence
  • Secant Methods - Broyden's method, updates, implementation with quasi-Newton methods, convergence
  • Specific Applications According to the Instructor's Interests