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An Attack on the Curse of Dimensionality
Colloquium| Speaker: | Dr. Martin Mohlenkamp, Dept. Applied Math., University of Colorado, Boulder, |
| Location: | 693 Kerr |
| Start time: | Tue, Apr 10 2001, 4:10PM |
Description
If it takes N samples to represent a function on an interval, then it
will take N^2 samples to represent an analogous function on a square,
and N^3 samples for one on a cube. Multiplying matrices in 1D takes
N^3 operations, in 2D it takes N^6, and in 3D it takes N^9. In
general, a computation that requires E effort in 1D will require E^d
effort in dimension d. This effect is known as the Curse of
Dimensionality and is the single greatest impediment to performing
realistic computations when d>2.
We are developing a technique to bypass the curse. Although at root it
is a simple generalization of separation of variables, it provides an
important conceptual framework for computing in higher dimensions.
This framework is like the idea "banded matrix", which in itself
solves nothing, and "most" of the time is not applicable, but is still
extremely useful for many problems.
Refreshment is served at 693 Kerr at 3:45pm