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{\large Naveen Somasunderam \\
{\bf Novel factorizations of discrete PDEs. }}

ECE Department \\ University of California \\ Santa Barbara \\ Santa Barbara \\ CA 93106
\\
{\tt naveen@umail.ucsb.edu}\\
Shiv Chandrasekaran\\
Ming Gu\\
Patrick Dewilde\\
Karthik Raghuram\end{center}

In this talk we look at the Cholesky factorizations in the limit of
infinitesimal grids of finite difference discretizations
of Elliptic PDEs. In particular, we show that the Schur complements of
these operators have point-wise limits. This in turn allows us to
consider new ways of constructing fast algorithms for these problems.

In particular, it can be shown that these operators can be written as an
$L SL^{T}$ factorization, where $L$ is lower triangular and $S$ has
diagonal plus semiseparable structure. These ideas lead to new ways of
factorizing the underlying operator with better conditioning properties.


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