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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 |
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