ditsol_pcg 

Preconditioned conjugate gradient method (Serial and Parallel Versions)

FORMAT

  DITSOL_PCG (matvec, pcondl, pcondr, mstop, a, ia, x, b, n,
              ql, iql , qr, iqr, iparam, rparam, iwork, rwork, ierror)

Arguments

  DITSOL_PCG has the standard parameter list for an iterative solver.

Description

  DITSOL_PCG implements the conjugate gradient method [Hestenes and Stiefel
  1952, Reid 1971] for the solution of a linear system of equations where the
  coefficient matrix A is symmetric positive definite or mildly nonsymmetric.
  This method requires the routine MATVEC to provide operations for job = 0.
  The routines MATVEC, PCONDL (if used) and MSTOP (if used) should be
  declared external in your calling (sub)program. PCONDR is not used by
  DITSOL_PCG and is therefore a dummy input parameter.

  CXML provides the following two forms of the method:

  •  Unpreconditioned conjugate gradient method:

     This is the conjugate gradient method applied to
          A * x = b
     where A is a symmetric positive definite or a mildly nonsymmetric
     matrix. As no preconditioning is used, both PCONDL and PCONDR are dummy
     input parameters.

     For the unpreconditioned conjugate gradient method, the length of the
     real work space array, defined by the variable nrwk (IPARAM(4)), should
     be at least 3*n, where n is the  order of the matrix A.

     The vector z, passed as an input argument to the routine MSTOP, is not
     defined.

  •  Conjugate gradient method with symmetric positive definite split
     preconditioning:

     This is the conjugate gradient method applied to

         (inverse(QL) * A * inverse(transp(QL)) ) * (transp(QL) * x) =
               (inverse(QL) * b)

     where

          Q = QL * transp(QL)

     is the symmetric positive definite preconditioning matrix.  The routine
     PCONDL, with job= 0 should evaluate

         v = inverse(Q) * u
     The routine PCONDR is not used and an explicit split of the
     preconditioner Q into QL and QR is not required.

     For the conjugate gradient method, with symmetric positive  definite
     split preconditioning, the length of the real work  space array, defined
     by the variable nrwk (IPARAM(4)), should  be at least 4*n, where n is
     the order of the matrix A. This does not include the memory requirements
     of the preconditioner.

     The vector z, passed as an input argument to the routine MSTOP, is
     defined as

         z = inverse(Q) * r

     where r is the residual at the i-th iteration.

  This routine is available in both serial and parallel versions. The routine
  names and parameter list are identical for both versions. For information
  about linking to the serial or to the parallel library, refer to the CXML
  Reference Manual.