HP MLIB User's Guide Vol. 2 7th Ed.

772 HP MLIB LAPACK User’s Guide
pdgssvx/ pzgssvx, pdgssvx_ABglobal/pzgssvx_ABglobal Solve systems of linear equations
Name pdgssvx/ pzgssvx, pdgssvx_ABglobal/pzgssvx_ABglobal
Solve systems of linear equations
Purpose
pdgssvx/pzgssvx and pdgssvx_ABglobal/pzgssvx_ABglobal solve systems of
linear equations AX=B. They perform the following functions:
• Equilibrate the system (scale A’s rows and columns to have unit norm) if A
is poorly scaled.
• Find a row permutation that makes diagonal of A large relative to the
off-diagonal.
• Find a column permutation that preserves the sparsity of the L and U
factors.
• Solve the system AX=B for X by factoring A followed by forward and back
substitutions.
• Refine the solution X.
Here are the options for using these routines:
1. Independent of all the other options specified below, the user must supply:
• B, the matrix of right hand sides, and its dimensions ldb and nrhs.
NOTE ldb is local for pdgssvx and pzgssvx, and global for pdgssvx_ABglobal
and pzgssvx_ABglobal.
• grid, a structure describing the 2D processor mesh.
• options->IterRefine, which determines whether or not to improve the
accuracy of the computed solution using iterative refinement.
2. Depending on options->Fact, the user has several options for solving AX=B.
The standard option is for factoring A from scratch. (The other options,
described below, are used when A is sufficiently similar to a previously
solved problem to save time by reusing part or all of the previous
factorization.)
• options->Fact = DOFACT: A is factored from scratch.
In this case the user must also supply:
• A, the input matrix
as well as the following options, which are described in more detail below:
• options->Equil, to specify how to scale the rows and columns of A to
equilibrate it (to try to reduce its condition number and so improve the
accuracy of the computed solution).