http:^^www.cs.indiana.edu^hyplan^dswise^quadtreematrices.html

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Date: Wed, 20 Nov 1996 19:14:38 GMT
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<HTML><HEAD><TITLE>Algorithms for Quadtree Representation of Matrices</TITLE><LINK REV="made" HREF="mailto:dswise@cs.indiana.edu"></HEAD><BODY><H2>Algorithms for Quadtree Representation of Matrices</H2><STRONG>Description:</STRONG><BLOCKQUOTE>Rather than decomposing matrices into rows, columns or tiny blocks,we decompose them	<!WA0><A HREF="ftp://ftp.cs.indiana.edu/pub/techreports/TR357.ps.Z">recursively into quadrants.	</A>The array becomes a tree which still might be stored sequentially,and decompostion of the problem for multiprocessingfollows the subtrees.We explore this structureas an exercise of the thesis that functional programmingis ideal for multiprocessing;the resulting algorithms are expressed in C for better performance.<BLOCKQUOTE></BLOCKQUOTE>Opportunites for ``new'' algorithms abound.Sparse matrices have many empty subtrees, and simple algebra there;so, uniform algorithms can be applied to both sparse and nonsparse problems.Search problems (e.g. pivoting) steer by summaryinformation that ``decorates'' interior nodes of the tree.Under Gaussian elimination, a nonsingular subtree of any ordercan be eliminated at any step;the resulting	<!WA1><a href="ftp://ftp.cs.indiana.edu/pub/techreports/TR418.ps.Z">``undulant'' pivoting	</a>has been developedfor bothexact and	<!WA2><a href="ftp://ftp.cs.indiana.edu/pub/techreports/TR433.ps.Z">floating-point decomposition	</a>.</BLOCKQUOTE><P><STRONG>Associated Faculty:</STRONG>	<!WA3><a href="http://www.cs.indiana.edu/hyplan/dswise.html">David S. Wise	</a>(	<!WA4><a href="mailto:dswise@cs.indiana.edu">dswise	</a>),	<!WA5><a href="http://www.cs.indiana.edu/hyplan/bramley.html">Randall Bramley	</a>(	<!WA6><a href="mailto:bramley@cs.indiana.edu">bramley	</a>).<P><STRONG>Associated Graduate Students:</STRONG>	<!WA7><a href="http://www.cs.indiana.edu/hyplan/jfrens.html">Jeremy Frens	</a>(	<!WA8><a href="mailto:jfrens@cs.indiana.edu">jfrens	</a>).<P><!-- OPTIONAL<STRONG>Affiliated Projects:</STRONG>List any affiliated projects, here or elsewhere, or people at otherplaces involved in the research.  Delete item if not applicable.<P>--><STRONG>Support:</STRONG>Supported in part by the        <!WA9><a href="http://www.nsf.gov">National Science Foundation        </a>under        <!WA10><a href="http://www.nsf.gov:80/cise/cda/in-infra.htm">a grant        </a>numbered        <!WA11><a href="http://www.cs.indiana.edu/hyplan/RI92.html">CDA93-03189        </a>.<P><!-- OPTIONAL<STRONG><!WA12><A HREF="http://www.cs.indiana.edu/hyplan/dswise/your_link.html">More information</A></STRONG><P>--><!WA13><A HREF="http://www.cs.indiana.edu/l/www/research/index.html"><!WA14><IMG SRC="http://www.cs.indiana.edu/hyplan/back.gif">Return to IU Computer ScienceResearch</A><!-- or use HREF="http://www.cs.indiana.edu/research/index.html" if your     page isn't served by the CS Dept server --></BODY></HTML>

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