TITLE:

SOLVING POLYNOMIAL SYSTEMS WITH SINGULAR SOLUTIONS (No. 99)

DATE:

Friday, February 3rd, 2006

TIME:

3:30 PM

LOCATION:

GMCS 214

SPEAKER:

Anton Leykin, Math Faculty Candidate, Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago

ABSTRACT:

In this talk I will describe a deflation algorithm used in solving systems of polynomial equations with complex coefficients by means of homotopy continuation methods. Using standard bases with respect to local monomial orderings, it is proved that the number of deflation steps needed to regularize a singular isolated solution is bounded by its multiplicity.

This technique combines ideas from symbolic computation and numerical analysis and falls naturally into the area of Numerical Algebraic Geometry. It will serve as a key ingredient in a numerical primary decomposition algorithm that will be developed in the near future.

HOST:

Robert Grone

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