Homework 7 Task 8: Preconditioning Strategies
Task: Look for internet sites that include descriptions of preconditioning of systems of equations. Document at least 3 different preconditioning strategies.
Preconditioning
Iterative methods, and the convergence of such methods, are heavily reliant on well-conditioned systems. If a system is poorly conditioned, then the system may not converge to a solution at all (or it will converge to an incorrect system). Thus, a preconditioning matrix can be applied to the original system of equations i.e.:
The condition number for BA may then be smaller than the condition number of A alone[1]. This also presents the requirement for preconditioners that they must[2]:
- Have better convergence than the original system
- Operations with B should be easy to perform
Different preconditioning strategies include: