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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.
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