INVESTIGADORES
DE LEO Mariano Fernando
artículos
Título:
Numeric vs. symbolic homotopy algorithms in polynomial system solving: a case study
Autor/es:
M. DE LEO; E. DRATMAN; G. MATERA
Revista:
JOURNAL OF COMPLEXITY
Editorial:
Academic Press
Referencias:
Lugar: Orlando, U.S.A.; Año: 2005 vol. 21 p. 502 - 535
ISSN:
0885-064X
Resumen:
We consider a family of polynomial systems which arises in the analysis of the stationary solutions of a standard discretization of certain semi-linear 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 behavior of all known symbolic algorithms solving a generic instance of this family of systems.
