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<BR> <P>
<P><A NAME="SECTIONREF"><H2>References</H2></A><P>
<DL COMPACT>
<DT><A NAME="aboelaze91a"><STRONG>1</STRONG></A><DD>
M. A<font size=-1><small>BOELAZE</small></font>, N. C<font size=-1><small>HRISOCHOIDES</small></font>, <font size=-1><small>AND</small></font> E. H<font size=-1><small>OUSTIS</small></font>, <EM>The Parallelization
of Level 2 and 3 BLAS Operations on Distributed Memory Machines</EM>, Tech. Rep.
CSD-TR-91-007, Purdue University, West Lafayette, IN, 1991.
<P>
<DT><A NAME="agarwal94b"><STRONG>2</STRONG></A><DD>
R. A<font size=-1><small>GARWAL</small></font>, F. G<font size=-1><small>USTAVSON</small></font>, <font size=-1><small>AND</small></font> M. Z<font size=-1><small>UBAIR</small></font>, <EM>Improving Performance of
Linear Algebra Algorithms for Dense Matrices Using Algorithmic Prefetching</EM>,
IBM J. Res. Dev., 38 (1994), pp. 265-275.
<P>
<DT><A NAME="laug"><STRONG>3</STRONG></A><DD>
E. A<font size=-1><small>NDERSON</small></font>, Z. B<font size=-1><small>AI</small></font>, C. B<font size=-1><small>ISCHOF</small></font>, J. D<font size=-1><small>EMMEL</small></font>, J. D<font size=-1><small>ONGARRA</small></font>, J. D<font size=-1><small>U</small></font> C<font size=-1><small>ROZ</small></font>, A. G<font size=-1><small>REENBAUM</small></font>, S. H<font size=-1><small>AMMARLING</small></font>, A. M<font size=-1><small>C</small></font>K<font size=-1><small>ENNEY</small></font>, S. O<font size=-1><small>STROUCHOV</small></font>, <font size=-1><small>AND</small></font> D. S<font size=-1><small>ORENSEN</small></font>,
<EM>LAPACK Users' Guide</EM>, Society for Industrial and Applied Mathematics,
Philadelphia, PA, second ed., 1995.
<P>
<DT><A NAME="lawn20"><STRONG>4</STRONG></A><DD>
E. A<font size=-1><small>NDERSON</small></font>, Z. B<font size=-1><small>AI</small></font>, C. B<font size=-1><small>ISCHOF</small></font>, J. D<font size=-1><small>EMMEL</small></font>, J. D<font size=-1><small>ONGARRA</small></font>, J. D<font size=-1><small>U</small></font> C<font size=-1><small>ROZ</small></font>, A. G<font size=-1><small>REENBAUM</small></font>, S. H<font size=-1><small>AMMARLING</small></font>, A. M<font size=-1><small>C</small></font>K<font size=-1><small>ENNEY</small></font>, <font size=-1><small>AND</small></font> D. S<font size=-1><small>ORENSEN</small></font>, <EM>LAPACK: A
portable linear algebra library for high-performance computers</EM>, Computer
Science Dept. Technical Report CS-90-105, University of Tennessee,
Knoxville, TN, May 1990.
(Also LAPACK Working Note #20).
<P>
<DT><A NAME="lawn31"><STRONG>5</STRONG></A><DD>
E. A<font size=-1><small>NDERSON</small></font>, Z. B<font size=-1><small>AI</small></font>, <font size=-1><small>AND</small></font> J. D<font size=-1><small>ONGARRA</small></font>, <EM>Generalized QR factorization
and its applications</EM>, Linear Algebra and Its Applications, 162-164 (1992),
pp. 243-273.
(Also LAPACK Working Note #31).
<P>
<DT><A NAME="angus90a"><STRONG>6</STRONG></A><DD>
I. A<font size=-1><small>NGUS</small></font>, G. F<font size=-1><small>OX</small></font>, J. K<font size=-1><small>IM</small></font>, <font size=-1><small>AND</small></font> D. W<font size=-1><small>ALKER</small></font>, <EM>Solving Problems on
Concurrent Processors: Software for Concurrent Processors</EM>, vol. 2, Prentice
Hall, Englewood Cliffs, N.J, 1990.
<P>
<DT><A NAME="ieee754"><STRONG>7</STRONG></A><DD>
ANSI/IEEE, <EM>
IEEE Standard for Binary Floating Point Arithmetic</EM>, New York, Std
754-1985 ed., 1985.
<P>
<DT><A NAME="ieee854"><STRONG>8</STRONG></A><DD>
height 2pt depth -1.6pt width 23pt, <EM>
IEEE Standard for Radix Independent Floating Point Arithmetic</EM>, New
York, Std 854-1987 ed., 1987.
<P>
<DT><A NAME="ariolidemmelduff"><STRONG>9</STRONG></A><DD>
M. A<font size=-1><small>RIOLI</small></font>, J. W. D<font size=-1><small>EMMEL</small></font>, <font size=-1><small>AND</small></font> I. S. D<font size=-1><small>UFF</small></font>, <EM>Solving sparse linear
systems with sparse backward error</EM>, SIAM J. Matrix Anal. Appl., 10 (1989),
pp. 165-190.
<P>
<DT><A NAME="ashcraft90a"><STRONG>10</STRONG></A><DD>
C. A<font size=-1><small>SHCRAFT</small></font>, <EM>The Distributed Solution of Linear Systems Using the
Torus-wrap Data mapping</EM>, Tech. Rep. ECA-TR-147, Boeing Computer Services,
Seattle, WA, 1990.
<P>
<DT><A NAME="bai92a"><STRONG>11</STRONG></A><DD>
Z. B<font size=-1><small>AI</small></font> <font size=-1><small>AND</small></font> J. D<font size=-1><small>EMMEL</small></font>, <EM>Design of a parallel nonsymmetric
eigenroutine toolbox, Part I</EM>, in Proceedings of the Sixth SIAM
Conference on Parallel Processing for Scientific Computing, SIAM, 1993,
pp. 391-398.
<P>
<DT><A NAME="baidemmel97"><STRONG>12</STRONG></A><DD>
Z. B<font size=-1><small>AI</small></font> <font size=-1><small>AND</small></font> J. D<font size=-1><small>EMMEL</small></font>, <EM>Using the matrix sign function to compute
invariant subspaces</EM>, SIAM J. Matrix Anal. Appl, x (1997), p. xxx.
to appear.
<P>
<DT><A NAME="lawn91"><STRONG>13</STRONG></A><DD>
Z. B<font size=-1><small>AI</small></font>, J. D<font size=-1><small>EMMEL</small></font>, J. D<font size=-1><small>ONGARRA</small></font>, A. P<font size=-1><small>ETITET</small></font>, H. R<font size=-1><small>OBINSON</small></font>, <font size=-1><small>AND</small></font> K. S<font size=-1><small>TANLEY</small></font>,
<EM>The spectral decomposition of nonsymmetric matrices on distributed
memory computers</EM>, Computer Science Dept. Technical Report
CS-95-273, University of Tennessee, Knoxville, TN, 1995.
(Also LAPACK Working Note No. 91), To appear in SIAM J. Sci.
Stat. Comput.
<P>
<DT><A NAME="baidemmel92a"><STRONG>14</STRONG></A><DD>
Z. B<font size=-1><small>AI</small></font> <font size=-1><small>AND</small></font> J. W. D<font size=-1><small>EMMEL</small></font>, <EM>Design of a parallel nonsymmetric
eigenroutine toolbox, Part I</EM>, in Proceedings of the Sixth SIAM
Conference on Parallel Processing for Scientific Computing, R. F. <EM>et
al</EM>. Sincovec, ed., Philadelphia, PA, 1993, Society for Industrial and
Applied Mathematics, pp. 391-398.
Long version available as Computer Science Report CSD-92-718,
University of California, Berkeley, 1992.
<P>
<DT><A NAME="barlowdemmel"><STRONG>15</STRONG></A><DD>
J. B<font size=-1><small>ARLOW</small></font> <font size=-1><small>AND</small></font> J. D<font size=-1><small>EMMEL</small></font>, <EM>Computing accurate eigensystems of scaled
diagonally dominant matrices</EM>, SIAM J. Num. Anal., 27 (1990), pp. 762-791.
(Also LAPACK Working Note #7).
<P>
<DT><A NAME="lawn111"><STRONG>16</STRONG></A><DD>
J. B<font size=-1><small>ILMES</small></font>, K. A<font size=-1><small>SANOVIC</small></font>, J. D<font size=-1><small>EMMEL</small></font>, D. L<font size=-1><small>AM</small></font>, <font size=-1><small>AND</small></font> C. C<font size=-1><small>HIN</small></font>, <EM>Optimizing
matrix multiply using PHiPAC: A portable, high-performance, ANSI C
coding methodology</EM>, Computer Science Dept. Technical Report
CS-96-326, University of Tennessee, Knoxville, TN, 1996.
(Also LAPACK Working Note #111).
<P>
<DT><A NAME="BV89"><STRONG>17</STRONG></A><DD>
R. H. B<font size=-1><small>ISSELING</small></font> <font size=-1><small>AND</small></font> J. G. G. <font size=-1><small>VAN</small></font> <font size=-1><small>DE</small></font> V<font size=-1><small>ORST</small></font>, <EM>Parallel LU
decomposition on a transputer network</EM>, in Lecture Notes in Computer Science,
Number 384, G. A. van Zee and J. G. G. van de Vorst, eds.,
Springer-Verlag, 1989, pp. 61-77.
<P>
<DT><A NAME="blackford96a"><STRONG>18</STRONG></A><DD>
L. S. B<font size=-1><small>LACKFORD</small></font>, J. C<font size=-1><small>HOI</small></font>, A. C<font size=-1><small>LEARY</small></font>, J. D<font size=-1><small>EMMEL</small></font>, I. D<font size=-1><small>HILLON</small></font>, J. J. D<font size=-1><small>ONGARRA</small></font>, S. H<font size=-1><small>AMMARLING</small></font>, G. H<font size=-1><small>ENRY</small></font>, A. P<font size=-1><small>ETITET</small></font>, K. S<font size=-1><small>TANLEY</small></font>, D. W. W<font size=-1><small>ALKER</small></font>, <font size=-1><small>AND</small></font> R. C. W<font size=-1><small>HALEY</small></font>, <EM>ScaLAPACK: A portable linear algebra library for
distributed memory computers - design issues and performance</EM>, in Proceedings
of Supercomputing '96, Sponsored by ACM SIGARCH and IEEE Computer Society,
1996.
(ACM Order Number: 415962, IEEE Computer Society Press Order Number:
RS00126. http://www.supercomp.org/sc96/proceedings/).
<P>
<DT><A NAME="lawn112"><STRONG>19</STRONG></A><DD>
L. S. B<font size=-1><small>LACKFORD</small></font>, A. C<font size=-1><small>LEARY</small></font>, J. D<font size=-1><small>EMMEL</small></font>, I. D<font size=-1><small>HILLON</small></font>, J. D<font size=-1><small>ONGARRA</small></font>, S. H<font size=-1><small>AMMARLING</small></font>, A. P<font size=-1><small>ETITET</small></font>, H. R<font size=-1><small>EN</small></font>, K. S<font size=-1><small>TANLEY</small></font>, <font size=-1><small>AND</small></font> R. C. W<font size=-1><small>HALEY</small></font>, <EM>
Practical experience in the dangers of heterogeneous computing</EM>, Computer
Science Dept. Technical Report CS-96-330, University of Tennessee,
Knoxville, TN, July 1996.
(Also LAPACK Working Note #112), to appear ACM Trans. Math. Softw.,
1997.
<P>
<DT><A NAME="brent92a"><STRONG>20</STRONG></A><DD>
R. B<font size=-1><small>RENT</small></font>, <EM>The LINPACK Benchmark on the AP 1000</EM>, in Frontiers,
1992, McLean, VA, 1992, pp. 128-135.
<P>
<DT><A NAME="brent93a"><STRONG>21</STRONG></A><DD>
R. B<font size=-1><small>RENT</small></font> <font size=-1><small>AND</small></font> P. S<font size=-1><small>TRAZDINS</small></font>, <EM>Implementation of BLAS Level 3 and
LINPACK Benchmark on the AP1000</EM>, Fujitsu Scientific and Technical Journal,
5 (1993), pp. 61-70.
<P>
<DT><A NAME="netlib1"><STRONG>22</STRONG></A><DD>
S. B<font size=-1><small>ROWNE</small></font>, J. D<font size=-1><small>ONGARRA</small></font>, S. G<font size=-1><small>REEN</small></font>, E. G<font size=-1><small>ROSSE</small></font>, K. M<font size=-1><small>OORE</small></font>, T. R<font size=-1><small>OWAN</small></font>, <font size=-1><small>AND</small></font> R. W<font size=-1><small>ADE</small></font>, <EM>Netlib services and resources (rev. 1)</EM>, Computer Science
Dept. Technical Report CS-94-222, University of Tennessee, Knoxville,
TN, 1994.
<P>
<DT><A NAME="netlib2"><STRONG>23</STRONG></A><DD>
S. B<font size=-1><small>ROWNE</small></font>, J. D<font size=-1><small>ONGARRA</small></font>, E. G<font size=-1><small>ROSSE</small></font>, <font size=-1><small>AND</small></font> T. R<font size=-1><small>OWAN</small></font>, <EM>The netlib
mathematical software repository</EM>, D-Lib Magazine (www.dlib.org), (1995).
<P>
<DT><A NAME="lawn93"><STRONG>24</STRONG></A><DD>
J. C<font size=-1><small>HOI</small></font>, J. D<font size=-1><small>EMMEL</small></font>, I. D<font size=-1><small>HILLON</small></font>, J. D<font size=-1><small>ONGARRA</small></font>, S. O<font size=-1><small>STROUCHOV</small></font>, A. P<font size=-1><small>ETITET</small></font>, K. S<font size=-1><small>TANLEY</small></font>, D. W<font size=-1><small>ALKER</small></font>, <font size=-1><small>AND</small></font> R. C. W<font size=-1><small>HALEY</small></font>, <EM>Installation guide for
ScaLAPACK</EM>, Computer Science Dept. Technical Report CS-95-280,
University of Tennessee, Knoxville, TN, March 1995.
(Also LAPACK Working Note #93).
<P>
<DT><A NAME="lawn95"><STRONG>25</STRONG></A><DD>
height 2pt depth -1.6pt width 23pt, <EM>ScaLAPACK: A
portable linear algebra library for distributed memory computers - design
issues and performance</EM>, Computer Science Dept. Technical Report
CS-95-283, University of Tennessee, Knoxville, TN, March 1995.
(Also LAPACK Working Note #95).
<P>
<DT><A NAME="lawn100"><STRONG>26</STRONG></A><DD>
J. C<font size=-1><small>HOI</small></font>, J. D<font size=-1><small>ONGARRA</small></font>, S. O<font size=-1><small>STROUCHOV</small></font>, A. P<font size=-1><small>ETITET</small></font>, D. W<font size=-1><small>ALKER</small></font>, <font size=-1><small>AND</small></font> R. C. W<font size=-1><small>HALEY</small></font>, <EM>A proposal for a set of parallel basic linear algebra
subprograms</EM>, Computer Science Dept. Technical Report CS-95-292,
University of Tennessee, Knoxville, TN, May 1995.
(Also LAPACK Working Note #100).
<P>
<DT><A NAME="lawn55"><STRONG>27</STRONG></A><DD>
J. C<font size=-1><small>HOI</small></font>, J. D<font size=-1><small>ONGARRA</small></font>, R. P<font size=-1><small>OZO</small></font>, <font size=-1><small>AND</small></font> D. W<font size=-1><small>ALKER</small></font>, <EM>ScaLAPACK: A
scalable linear algebra library for distributed memory concurrent computers</EM>,
in Proceedings of the Fourth Symposium on the Frontiers of Massively Parallel
Computation, McLean, Virginia, 1992, IEEE Computer Society Press,
pp. 120-127.
(Also LAPACK Working Note #55).
<P>
<DT><A NAME="lawn92"><STRONG>28</STRONG></A><DD>
J. C<font size=-1><small>HOI</small></font>, J. D<font size=-1><small>ONGARRA</small></font>, <font size=-1><small>AND</small></font> D. W<font size=-1><small>ALKER</small></font>, <EM>The design of a parallel dense
linear algebra software library: Reduction to Hessenberg, tridiagonal and
bidiagonal form</EM>, Numerical Algorithms, 10 (1995), pp. 379-399.
(Also LAPACK Working Note #92).
<P>
<DT><A NAME="choi94a"><STRONG>29</STRONG></A><DD>
J. C<font size=-1><small>HOI</small></font>, J. D<font size=-1><small>ONGARRA</small></font>, <font size=-1><small>AND</small></font> D. W<font size=-1><small>ALKER</small></font>, <EM>PB-BLAS: A Set of Parallel
Block Basic Linear Algebra Subroutines</EM>, Concurrency: Practice and
Experience, 8 (1996), pp. 517-535.
<P>
<DT><A NAME="chtchelkanova95a"><STRONG>30</STRONG></A><DD>
A. C<font size=-1><small>HTCHELKANOVA</small></font>, J. G<font size=-1><small>UNNELS</small></font>, G. M<font size=-1><small>ORROW</small></font>, J. O<font size=-1><small>VERFELT</small></font>, <font size=-1><small>AND</small></font> R. <font size=-1><small>VAN</small></font> <font size=-1><small>DE</small></font> G<font size=-1><small>EIJN</small></font>, <EM>Parallel Implementation of BLAS: General Techniques for Level 3
BLAS</EM>, Tech. Rep. TR95-49, Department of Computer Sciences, UT-Austin, 1995.
Submitted to Concurrency: Practice and Experience.
<P>
<DT><A NAME="chu90a"><STRONG>31</STRONG></A><DD>
E. C<font size=-1><small>HU</small></font> <font size=-1><small>AND</small></font> A. G<font size=-1><small>EORGE</small></font>, <EM>QR Factorization of a Dense Matrix on a
Hypercube Multiprocessor</EM>, SIAM Journal on Scientific and Statistical
Computing, 11 (1990), pp. 990-1028.
<P>
<DT><A NAME="lawn125"><STRONG>32</STRONG></A><DD>
A. C<font size=-1><small>LEARY</small></font> <font size=-1><small>AND</small></font> J. D<font size=-1><small>ONGARRA</small></font>, <EM>Implementation in scalapack of
divide-and-conquer algorithms for banded and tridiagonal linear systems</EM>,
Computer Science Dept. Technical Report CS-97-358, University of
Tennessee, Knoxville, TN, April 1997.
(Also LAPACK Working Note #125).
<P>
<DT><A NAME="cosnard86a"><STRONG>33</STRONG></A><DD>
M. C<font size=-1><small>OSNARD</small></font>, Y. R<font size=-1><small>OBERT</small></font>, P. Q<font size=-1><small>UINTON</small></font>, <font size=-1><small>AND</small></font> M. T<font size=-1><small>CHUENTE</small></font>, eds., <EM>Parallel
Algorithms and Architectures</EM>, North-Holland, 1986.
<P>
<DT><A NAME="berkeleynow"><STRONG>34</STRONG></A><DD>
D. E. C<font size=-1><small>ULLER</small></font>, A. A<font size=-1><small>RPACI</small></font>-D<font size=-1><small>USSEAU</small></font>, R. A<font size=-1><small>RPACI</small></font>-D<font size=-1><small>USSEAU</small></font>, B. C<font size=-1><small>HUN</small></font>, S. L<font size=-1><small>UMETTA</small></font>, A. M<font size=-1><small>AINWARING</small></font>, R. M<font size=-1><small>ARTIN</small></font>, C. Y<font size=-1><small>OSHIKAWA</small></font>, <font size=-1><small>AND</small></font> F. W<font size=-1><small>ONG</small></font>, <EM>Parallel computing
on the Berkeley NOW</EM>.
To appear in JSPP'97 (9th Joint Symposium on Parallel Processing),
Kobe, Japan, 1997.
<P>
<DT><A NAME="dayde94a"><STRONG>35</STRONG></A><DD>
M. D<font size=-1><small>AYDE</small></font>, I. D<font size=-1><small>UFF</small></font>, <font size=-1><small>AND</small></font> A. P<font size=-1><small>ETITET</small></font>, <EM>A Parallel Block Implementation
of Level 3 BLAS for MIMD Vector Processors</EM>, ACM Trans. Math. Softw., 20
(1994), pp. 178-193.
<P>
<DT><A NAME="demoorvandooren92"><STRONG>36</STRONG></A><DD>
B. D<font size=-1><small>E</small></font> M<font size=-1><small>OOR</small></font> <font size=-1><small>AND</small></font> P. V<font size=-1><small>AN</small></font> D<font size=-1><small>OOREN</small></font>, <EM>Generalization of the singular value
and QR decompositions</EM>, SIAM J. Matrix Anal. Appl., 13 (1992),
pp. 993-1014.
<P>
<DT><A NAME="demmel84"><STRONG>37</STRONG></A><DD>
J. D<font size=-1><small>EMMEL</small></font>, <EM>Underflow and the reliability of numerical software</EM>,
SIAM J. Sci. Stat. Comput., 5 (1984), pp. 887-919.
<P>
<DT><A NAME="demmelMA221"><STRONG>38</STRONG></A><DD>
height 2pt depth -1.6pt width 23pt, <EM>Applied Numerical
Linear Algebra</EM>, SIAM, 1996.
to appear.
<P>
<DT><A NAME="demmeleisenstatgilbertliliu"><STRONG>39</STRONG></A><DD>
J. D<font size=-1><small>EMMEL</small></font>, S. E<font size=-1><small>ISENSTAT</small></font>, J. G<font size=-1><small>ILBERT</small></font>, X. L<font size=-1><small>I</small></font>, <font size=-1><small>AND</small></font> J. W. H. L<font size=-1><small>IU</small></font>, <EM>A
supernodal approach to sparse partial pivoting</EM>, Technical Report
UCB//CSD-95-883, UC Berkeley Computer Science Division, September 1995.
to appear in SIAM J. Mat. Anal. Appl.
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<DT><A NAME="lawn86"><STRONG>40</STRONG></A><DD>
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<DT><A NAME="wilkinson1"><STRONG>114</STRONG></A><DD>
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</DL>
<P>
<BR> <HR>
<P><ADDRESS>
<I>Susan Blackford <BR>
Tue May 13 09:21:01 EDT 1997</I>
</ADDRESS>
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