Numeric vs. symbolic homotopy algorithms in polynomial system solving: a case study

Abstract

We consider a family of polynomial systems which arises in the analysis of the stationary solutions of a standard discretization of certain semilinear second order parabolic partial differential equations. We prove that this family is well–conditioned from the numeric point of view, and ill–conditioned from the symbolic point of view. We exhibit a polynomial–time numeric algorithm solving any member of this family, which significantly contrasts the exponential behaviour of all known symbolic algorithms solving a generic instance of this family of systems.

DOI: 10.1016/j.jco.2004.09.008

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Cite this paper

@article{Leo2005NumericVS, title={Numeric vs. symbolic homotopy algorithms in polynomial system solving: a case study}, author={Mariano De Leo and Ezequiel Dratman and Guillermo Matera}, journal={J. Complexity}, year={2005}, volume={21}, pages={502-531} }