Direct Methods for Sparse Linear Systems: The MATLAB sparse backslash
Length: 42 minutes. Click the image above to watch it on YouTube.
- This was a plenary talk given at the
SIAM Annual Meeting, Boston, 2006.
Sparse linear systems arise in a wide range of problems in computational science, including such diverse topics as circuit simulation, semiconductor process simulation, DNA electrophoresis, structural mechanics, computational fluid dynamics, and financial portfolio optimization. Direct methods for solving these systems rely on an elegant combination of graph algorithms and linear algebra: elimination trees, depth-first search, paths, cycles, chords, topological orderings, heuristics for NP-hard problems, cliques, cache-friendly dense matrix kernels, graph partitioning, and more. Sparse matrix methods and theory are presented in depth via a simple and concise pair of algorithms for sparse LU and Cholesky factorization, starting from basic principles. Multifrontal and supernodal methods that accelerate these basic algorithms are then illustrated; both are used in x=A\b in MATLAB.
- SIAM had wanted to record the talk, but due to a minor technical glitch, the audio feed failed.
The talk posted here is the same as the one given at the SIAM conference. It was presented
as part of the
G2V2 seminar series in the
CISE Department of the
University of Florida.
- This talk will be available soon on the SIAM web page.
- Click here for the talk in MPEG, 589MB in length.
In this version, the text on the screen is more easily readable.
- Click here for the talk in WMV, 41MB in length.
Use this if you have a slow connection or if you are low on disk space.
- The complete slides (PDF).
- Just the primary slides (PDF). This compact version is
suitable for printing (to print in Adobe Reader, select "multiple
pages per sheet" for the page-scaling option, and print 3-by-4 pages
per sheet). Since the slides can be hard to see sometimes in the video (particularly the
lower resolution versions), I suggest that you view the PDF file on-line, or print it out,
and refer to it while you view the video.
- This talk is a concise synopsis of the book
Direct Methods for Sparse Linear Systems
"the sparse backslash book"),
published by SIAM.
- I would like to thank
Cleve Moler, and the members of
for inviting me to give this talk at the SIAM meeting.
I would also like to thank
(one of my PhD students) for videotaping the talk given in the G2V2 seminar.