Previous: The why and how
Up: Preconditioners
Next: SSOR preconditioning
Previous Page: Theoretical prerequisites on preconditioners
Next Page: Block Jacobi Methods

Jacobi Preconditioning

The simplest preconditioner consists of just the diagonal of the matrix:

This is known as the (point) Jacobi preconditioner.

It is possible to use this preconditioner without using any extra storage beyond that of the matrix itself. However, division operations are usually quite costly, so in practice storage is allocated for the reciprocals of the matrix diagonal. This strategy applies to many preconditioners below.