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\title{Cache Management for the IQMR Method on Massively Parallel Computers}

\author{\em Tianruo Yang $\dagger$, Hai-Xiang Lin $\ddagger$ \\ \em $\dagger$
  Department of Computer and Information Science \\ \em  Link\"oping
  University,  S-581 83, Link\"oping, Sweden \\
  \em $\ddagger$ Department of Technical Mathematics and Computer
  Science \\ \em TU Delft, P.O. Box 356, 2600 GA Delft, The Netherlands}
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\begin{abstract}
For the solutions of linear systems of equations with unsymmetric
coefficient sparse matrices, we have proposed an improved version of
the quasi-minimal residual (IQMR) method by rescheduling the algorithm
without changing numerical stability, but the algorithm is derived
such that all inner products and matrix-vector multiplications of a
single iteration step are independent and communication time required
for inner product can be overlapped efficiently with computation
time. Therefore, the cost of global communication on parallel
computers can be significantly reduced. In this paper, we mainly
investigate the efficient parallelization technique with regards to cache
management strategy, involving a cache mirror, for use in
matrix-vector multiplications. Use of the cache mirror allows our
IQMR parallel implementation to avoid cache conflicts and shows that
using noncached loads further avoids cache conflicts when accessing
nonreused data. The cache minor can be also used for vector updates
and inner products to get effect. From experimental results we
demonstrate around much better parallel performance over the conventional
Fortran or C implementation on RISC based MIMD massively parallel
computers.
\end{abstract}

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