Previous: Jacobi Preconditioning
Up: Preconditioners
Next: Incomplete Factorization Preconditioners
Previous Page: Discussion
Next Page: Incomplete Factorization Preconditioners
The SSOR preconditioner
like the Jacobi preconditioner, can be derived from the coefficient
matrix without any work.
If the original, symmetric, matrix is decomposed as
in its diagonal, lower, and upper triangular part, the SSOR matrix is defined as
or, parametrized by
The optimal value of the parameter, like the
parameter in the SOR method, will reduce the number
of iterations to a lower order. Specifically, the spectral
condition number
is attainable,
see Axelsson and Barker[14]. In practice,
however, the spectral
information needed to calculate the optimal
is prohibitively
expensive to compute.
The SSOR matrix is given in factored form, so this preconditioner
shares many properties of other factorization-based methods (see
below). For instance, its suitability for vector processors or
parallel architectures depends strongly on the
ordering of the variables. On the other hand, since this factorization
is given a priori, there is no possibility of breakdown as in
the construction phase of incomplete factorization methods.