NAG Library Function Document
nag_sparse_sym_precon_ssor_solve (f11jdc) 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.
||nag_sparse_sym_precon_ssor_solve (Integer n,
const double a,
const Integer irow,
const Integer icol,
const double rdiag,
const double y,
nag_sparse_sym_precon_ssor_solve (f11jdc) solves a system of equations
involving the preconditioning matrix
corresponding to symmetric successive-over-relaxation (SSOR) (see Young (1971)
) on a linear system
is a sparse symmetric matrix stored in symmetric coordinate storage (SCS) format (see Section 2.1.2
in the f11 Chapter Introduction).
In the definition of given above is the diagonal part of , is the strictly lower triangular part of , and is a user-defined relaxation argument.
It is envisaged that a common use of nag_sparse_sym_precon_ssor_solve (f11jdc) will be to carry out the preconditioning step required in the application of nag_sparse_sym_basic_solver (f11gec)
to sparse linear systems. For an illustration of this use of nag_sparse_sym_precon_ssor_solve (f11jdc) see the example program given in Section 9.1
. nag_sparse_sym_precon_ssor_solve (f11jdc) is also used for this purpose by the Black Box function nag_sparse_sym_sol (f11jec)
Young D (1971) Iterative Solution of Large Linear Systems Academic Press, New York
n – IntegerInput
, the order of the matrix .
nnz – IntegerInput
the number of nonzero elements in the lower triangular part of .
a[nnz] – const doubleInput
: the nonzero elements in the lower triangular part of the matrix
, ordered by increasing row index, and by increasing column index within each row. Multiple entries for the same row and column indices are not permitted. The function nag_sparse_sym_sort (f11zbc)
may be used to order the elements in this way.
irow[nnz] – const IntegerInput
icol[nnz] – const IntegerInput
: the row and column indices of the nonzero elements supplied in array a
must satisfy these constraints (which may be imposed by a call to nag_sparse_sym_sort (f11zbc)
- and , for ;
- or and , for .
rdiag[n] – const doubleInput
On entry: the elements of the diagonal matrix , where is the diagonal part of .
omega – doubleInput
On entry: the relaxation argument .
check – Nag_SparseSym_CheckDataInput
: specifies whether or not the input data should be checked.
- Checks are carried out on the values of n, nnz, irow, icol and omega.
- None of these checks are carried out.
y[n] – const doubleInput
On entry: the right-hand side vector .
x[n] – doubleOutput
On exit: the solution vector .
fail – NagError *Input/Output
The NAG error argument (see Section 3.6
in the Essential Introduction).
6 Error Indicators and Warnings
Dynamic memory allocation failed.
On entry, argument had an illegal value.
On entry, .
On entry, .
On entry, and .
An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG
On entry, , , .
Constraint: and .
On entry, , and .
Constraint: and .
On entry, is out of order:
On entry, the location (
) is a duplicate:
. Consider calling nag_sparse_sym_sort (f11zbc)
to reorder and sum or remove duplicates.
On entry, .
The matrix has no diagonal entry in row .
The computed solution
is the exact solution of a perturbed system of equations
is a modest linear function of
is the machine precision
The time taken for a call to nag_sparse_sym_precon_ssor_solve (f11jdc) is proportional to nnz
It is expected that a common use of nag_sparse_sym_precon_ssor_solve (f11jdc) will be to carry out the preconditioning step required in the application of nag_sparse_sym_basic_solver (f11gec)
to sparse symmetric linear systems. In this situation nag_sparse_sym_precon_ssor_solve (f11jdc) is likely to be called many times with the same matrix
. In the interests of both reliability and efficiency, you are recommended to set
for the first of such calls, and to set
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 function nag_sparse_sym_basic_solver (f11gec)
, which returns repeatedly to the calling program with various values of the argument irevcm
. This argument indicates the action to be taken by the calling program.
- If , a matrix-vector product is required. This is implemented by a call to nag_sparse_sym_matvec (f11xec).
- If , a solution of the preconditioning equation is required. This is achieved by a call to nag_sparse_sym_precon_ssor_solve (f11jdc).
- If , nag_sparse_sym_basic_solver (f11gec) has completed its tasks. Either the iteration has terminated, or an error condition has arisen.
For further details see the function document for nag_sparse_sym_basic_solver (f11gec)
9.1 Program Text
Program Text (f11jdce.c)
9.2 Program Data
Program Data (f11jdce.d)
9.3 Program Results
Program Results (f11jdce.r)