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<B> Next:</B> <A NAME="tex2html3672" HREF="node118.html">Solving Linear Least Squares </A>
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<H2><A NAME="SECTION04526000000000000000">Solving Linear Systems of Equations</A></H2>
     <A NAME="subseclin">&#160;</A>
<P>
Table&nbsp;<A HREF="node117.html#tabluperf">5.9</A><A NAME="3938">&#160;</A>
illustrates the speed of the ScaLAPACK driver
routine PSGESV<A NAME="3939">&#160;</A>/PDGESV<A NAME="3940">&#160;</A>
for solving a square linear system of order <I>N</I> by
LU factorization with partial row pivoting of a real
matrix. For all timings, 64-bit floating-point arithmetic was used.
Thus, single-precision timings are reported for
the Cray T3E, and double precision timings are reported
on all other computers.  The distribution block size<A NAME="3941">&#160;</A> is 
also used as the partitioning unit<A NAME="3942">&#160;</A> for the computation and
communication phases.
<P>
Table&nbsp;<A HREF="node117.html#tablltperf">5.10</A><A NAME="3944">&#160;</A>
illustrates the speed of the ScaLAPACK routine
PSPOSV<A NAME="3945">&#160;</A>/PDPOSV<A NAME="3946">&#160;</A> for
solving a symmetric positive definite linear system of
order <I>N</I> via the Cholesky factorization.
<P>
Right-looking variants of the <I>LU</I> and Cholesky factorizations
were chosen for ScaLAPACK because they minimize total communication
volume, that is, the aggregated
<P><A NAME="3948">&#160;</A><A NAME="tabluperf">&#160;</A><IMG WIDTH=747 HEIGHT=728 ALIGN=BOTTOM ALT="table3947" SRC="img396.gif"><BR>
<STRONG>Table 5.9:</STRONG> Speed in Mflop/s of PSGESV/PDGESV for square
          matrices of order <I>N</I><BR>
<P>
amount of data transferred between processes during the operation.
<P><A NAME="3970">&#160;</A><A NAME="tablltperf">&#160;</A><IMG WIDTH=747 HEIGHT=605 ALIGN=BOTTOM ALT="table3969" SRC="img397.gif"><BR>
<STRONG>Table 5.10:</STRONG> Speed in Mflop/s of PSPOSV/PDPOSV for matrices of
          order <I>N</I> with UPLO=`U'<BR>
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<UL><A NAME="CHILD_LINKS">&#160;</A>
<LI> <A NAME="tex2html3675" HREF="node118.html#SECTION04526100000000000000">Solving Linear Least Squares Problems</A>
<LI> <A NAME="tex2html3676" HREF="node119.html#SECTION04526200000000000000">Eigenvalue Problems</A>
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<P><ADDRESS>
<I>Susan Blackford <BR>
Tue May 13 09:21:01 EDT 1997</I>
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