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Title: The Discovery of Reduced Symbolic Models
and the Seven Dwarfs of Symbolic Computation
Speaker: Erich Kaltofen
Department of Mathematics and Department of Computer Science
North Carolina State University
Abstract:
The reconstruction of a function from a set of observed or computed
data points goes back at least to Gauss's least squares curve fitting.
A significant contribution of symbolic computation are algorithms for the
recovery of sparse polynomial models [Giesbrecht, Labahn, Lee 2003-6] and
of sparse rational function models [Kaltofen, Yang, Zhi 2007] from
reduced sets of data points. The underlying algebraic, randomized
algorithms are hybridized for noisy input data, thus complicating
the probabilistic analysis as the random projections now must avoid
ill-conditioned subproblems rather than exact singularities.
We will discuss the arising problems in random matrix theory, and present
the additional example of solving highly overdetermined dense linear systems
in nearly optimal complexity.
At http://view.eecs.berkeley.edu/wiki/Dwarf_Mine a Berkeley author team
proposes 13 "Dwarfs" (methods) of scientific problem solving. Kathy Yelick
has indicated to me that Symbolic Computation is another dwarf. I shall propose
7 "(sub)Dwarfs" of Symbolic Computation and their role in model discovery.
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