** Next:** Preconditioning Techniques
** Up:** Parallelism J. Dongarra and
** Previous:** Matrix-Vector Products.
** Contents**
** Index**

####

Solvers.

In addition to the three kernels above, the iterative methods using
shift-and-invert often require the direct solutions of the linear systems.
Both matrix factorization and triangular solve involve much
more complicated parallel algorithms,
especially on massively parallel machines.
There has been a large amount of research activity in this area.
Many state-of-the-art parallel algorithms for dense and band matrices are
implemented in ScaLAPACK (see § 10.3),
and those for sparse matrices are
implemented in the software packages surveyed in
Table 10.1.

Susan Blackford
2000-11-20