intro_solvers(3S)

NAME
     INTRO_SOLVERS - Introduction to SGI-developed linear equation solvers

IMPLEMENTATION
     See individual man pages for implementation information

DESCRIPTION
     SCSL provides two direct solvers, PSLDLT and PSLDU, and one iterative
     solver, DIterative for sparse linear systems of equations.  These solvers
     are optimized and parallelized for the SGI platforms.  For direct solvers
     for dense linear systems of equations, see the INTRO_LAPACK(3S) man page.

     DPSLDLT and ZPSLDLT solve sparse symmetric linear systems of the form Ax
     = b where A is an n-by-n symmetric input matrix, b is an input vector of
     length n, and x is a vector of unknowns of length n.

     The symmetric solver uses a direct method. A is factored into the
     following form:

          A = L D LT

     where L is a lower triangular matrix with unit diagonal and D is a
     diagonal matrix.

     The symmetric solver supports both real and complex double precision data
     types and is available in the multi-processing versions of SCSL.  See the
     DPSLDLT(3S) and ZPSLDLT(3S) man pages for details.

     DPSLDU and ZPSLDU solve sparse unsymmetric linear systems of the form Ax
     = b where A is an n-by-n input matrix with symmetric non-zero pattern but
     unsymmetric non-zero values, b is an input vector of length n, and x is a
     vector of unknowns of length n.

     The unsymmetric solver uses a direct method. A is factored into the
     following form:

          A = L D U

     where L is a lower triangular matrix with unit diagonal, D is a diagonal
     matrix, and U is an upper triangular matrix with unit diagonal.

     The unsymmetric solver supports both real and complex double precision
     data types and is available in the multi-processing versions of SCSL. See
     the DPSLDU(3S) and ZPSLDU(3S) man pages for details.

     DIterative solves sparse linear systems of the form Ax = b where A is a
     n-by-n sparse input matrix in Compressed Sparse Column (CSC) or
     Compressed Sparse Row (CSR) format, b is an input vector of length n, and
     x is a vector of unknowns of length n.
     The iterative solver uses on of four preconditioned iterative methods:
     conjugate gradient (CG) and conjugate residual (CR) for symmetric
     systems, and conjugate gradient squared (CGS) and BiCGSTAB, a variant of
     of CGS with smoother convergence properties,  for unsymmetric systems.
     Four different types of preconditioners are available: Jacobi, symmetric
     successive over-relaxation (SSOR), ILDLT (incomplete LDLT) by pattern,
     and ILDLT by value. The ILDLT preconditioners are only available for
     symmetric matrices, and ILDLT by value is currently not parallel.

     The iterative solver supports only real double precision data.  See the
     ITERATIVE(3S) man page for details.

NOTES
     No pivoting is done in the direct sparse solver routines.

     SCSL does not currently support reshaped arrays.

SEE ALSO
     INTRO_SCSL(3S), INTRO_LAPACK(3S)