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Computation of Accurate Eigenvalues and its Applications - from Electrical Impedance Tomography to 3D Target Recognition
Special Events| Speaker: | Plamen Koev, Massachusetts Institute of Technology |
| Location: | 1147 MSB |
| Start time: | Wed, Feb 7 2007, 4:10PM |
Description
Eigenvalue computation has pervasive applications across most branches of
science and engineering. In this talk I will present our recent highly
accurate and efficient algorithms for structured eigenvalue problems.
In finite precision computations the accuracy of the tiniest eigenvalues
can quickly be lost to round-off errors. This is unfortunate since these
tiny eigenvalues are often very accurately determined by the data and are
of considerable physical significance. For example, in Electrical
Impedance Tomography, the SVD of a particular Vandermonde matrix allows us
to recover the conductivity of the interior of an object. A similar
approach in inverse scattering gives rise to the same computational
problem. Another example is 3D target recognition in which the
eigenvalues of the covariance matrix of a vehicle's 3D coordinates become
the 'signature' that can be used to recognize the vehicle; this method is
independent of the angle of observation and hence overcomes a major
drawback in two dimensions.
The foregoing applications are examples of problems that have benefited
immensely from the new highly accurate eigenvalue algorithms that we have
developed. Our algorithms, unlike the conventional ones, respect and
exploit the underlying combinatorial and algebraic matrix structure and
compute all eigenvalues to high relative accuracy without the need for
extra precision.
In the talk I will focus in particular on our new algorithm for computing
eigenvalues of random matrices, a computational problem whose solution has
eluded researchers for over 40 years.
Biographical Sketch
Dr. Koev did his doctoral work under the supervision of Professor James
Demmel and received his Ph.D. in mathematics from the University of
California, Berkeley in 2002. He is currently a postdoctoral researcher
in the mathematics department at M.I.T. His interests are in accurate and
efficient matrix computations, applied multivariate statistical analysis
and random matrix theory.