Parallel Constrained Least-Squares Solvers
Solving Constrained Least-Squares Systems
The routine PARALLEL_NONNEGATIVE_LSQ
is used to solve dense least-squares systems. These are represented by
where A is
an 
coefficient
data matrix, 
is a given
right-hand side 
-vector,
and 
is the
solution 
-vector being
computed. Further, there is a constraint requirement, 
. The routine PARALLEL_BOUNDED_LSQ
is used when the problem has lower and upper bounds for the solution,
. By making the
bounds large, individual constraints can be eliminated. There are no
restrictions on the relative sizes of and . When is large, these codes
can substantially reduce computer time and storage requirements, compared with
using a routine for solving a constrained system and a single processor.
The user provides the matrix partitioned by blocks of columns:
. An individual block of the partitioned matrix, say
, is located entirely
on the processor with rank 
, where MP_RANK
is packaged in the module MPI_SETUP_INT.
This module, and the function MP_SETUP(),define
the Fortran Library MPI communicator, MP_LIBRARY_WORLD.
See Chapter 10, Dense Matrix Parallelism Using MPI.
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