F11JDF solves a system of linear equations involving the preconditioning matrix corresponding to SSOR applied to a real sparse symmetric matrix, represented in symmetric coordinate storage format.
F11JDF solves a system of equations
involving the preconditioning matrix
corresponding to symmetric successive-over-relaxation (SSOR) (see
Young (1971)) on a linear system
Ax=b, where
A is a sparse symmetric matrix stored in symmetric coordinate storage (SCS) format (see
Section 2.1.2 in the F11 Chapter Introduction).
It is envisaged that a common use of F11JDF will be to carry out the preconditioning step required in the application of
F11GEF to sparse linear systems. For an illustration of this use of F11JDF see the example program given in
Section 9.1. F11JDF is also used for this purpose by the Black Box routine
F11JEF.
If on entry
IFAIL=0 or
-1, explanatory error messages are output on the current error message unit (as defined by
X04AAF).
The computed solution
x is the exact solution of a perturbed system of equations
M+δMx=y, where
cn is a modest linear function of
n, and
ε is the
machine precision.
The time taken for a call to F11JDF is proportional to
NNZ.
It is expected that a common use of F11JDF will be to carry out the preconditioning step required in the application of
F11GEF to sparse symmetric linear systems. In this situation F11JDF is likely to be called many times with the same matrix
M. In the interests of both reliability and efficiency, you are recommended to set
CHECK='C' for the first of such calls, and to set
CHECK='N' for all subsequent calls.
This example solves a sparse symmetric linear system of equations
using the conjugate-gradient (CG) method with SSOR preconditioning.
The CG algorithm itself is implemented by the reverse communication routine
F11GEF, which returns repeatedly to the calling program with various values of the parameter
IREVCM. This parameter indicates the action to be taken by the calling program.
- If IREVCM=1, a matrix-vector product v=Au is required. This is implemented by a call to F11XEF.
- If IREVCM=2, a solution of the preconditioning equation Mv=u is required. This is achieved by a call to F11JDF.
- If IREVCM=4, F11GEF has completed its tasks. Either the iteration has terminated, or an error condition has arisen.
For further details see the routine document for
F11GEF.