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- Jean-Pierre Dedieu, Michael Shub
- Math. Comput.
- 2000

Complexity theoretic aspects of continuation methods for the solution of square or underdetermined systems of polynomial equations have been studied by various authors. In this paper we considerâ€¦ (More)

- Jean-Pierre Dedieu, Gregorio Malajovich, Michael Shub
- Foundations of Computational Mathematics
- 2005

We prove a linear bound on the average total curvature of the central path of linear programming theory in terms on the number of independent variables of the primal problem, and independent of theâ€¦ (More)

We consider polynomial eigenvalue problems P(A, Î±, Î²)x = 0 in which the matrix polynomial is homogeneous in the eigenvalue (Î±, Î²) âˆˆ C2. In this framework infinite eigenvalues are on the same footingâ€¦ (More)

- Jean-Pierre Dedieu, Myong-Hi Kim
- J. Complexity
- 2002

In this paper, Smaleâ€™s Î± theory is generalized to the context of intrinsic Newton iteration on geodesically complete analytic Riemannian and Hermitian manifolds. Results are valid for analyticâ€¦ (More)

- Jean-Pierre Dedieu, Dmitry Nowicki
- J. Complexity
- 2005

We use a Hamiltonian approach and symplectic methods to compute the geodesics on a Riemannian submanifold. Â© 2005 Elsevier Inc. All rights reserved.

- Jean-Pierre Dedieu
- J. Symb. Comput.
- 1997

This paper is devoted to the study of the separation number of a polynomial system f : C â†’ C defining a zero-dimensional nonsingular variety. The separation number of f is defined by sep(f) = min â€–xâˆ’â€¦ (More)

- Jean-Pierre Dedieu, Jean-Claude Yakoubsohn
- Applicable Algebra in Engineering, Communicationâ€¦
- 1991

We describe a new algorithm for the localization of an algebraic hypersurfaceV inR n or Cn. This algorithm computes a decreasing sequence of closed sets whose intersection isV. In the particular caseâ€¦ (More)

- Jean-Pierre Dedieu, Michael Shub
- I. J. Bifurcation and Chaos
- 2005

In this paper we take up once again the subject of the geometry of the central paths of linear programming theory. We study the boundary behavior of these paths as in Meggido and Shub [5], but from aâ€¦ (More)

- Jean-Pierre Dedieu, Michael Shub
- Math. Comput.
- 2000

We study multihomogeneous analytic functions and a multihomogeneous Newtonâ€™s method for finding their zeros. We give a convergence result for this iteration and we study two examples: the evaluationâ€¦ (More)