33 citations · 33 across the 1 of their papers we have counts for
6 papers
Adaptative Step Size Selection for Homotopy Methods to Solve Polynomial Equations
Jean-Pierre Dedieu, Gregorio Malajovich, Michael Shub
Given a C^1 path of systems of homogeneous polynomial equations f_t, t in [a,b] and an approximation x_a to a zero zeta_a of the initial system f_a, we show how to adaptively choos…
Convexity properties of the condition number II
Carlos Beltrán, Jean-Pierre Dedieu, Gregorio Malajovich +1
In our previous paper [SIMAX 31 n.3 1491-1506(2010)], we studied the condition metric in the space of maximal rank matrices. Here, we show that this condition metric induces a Lips…
Convexity properties of the condition number
Carlos Beltrán, Jean-Pierre Dedieu, Gregorio Malajovich +1
We define in the space of n by m matrices of rank n, n less or equal than m, the condition Riemannian structure as follows: For a given matrix A the tangent space of A is equipped…
On the number of minima of a random polynomial
Jean-Pierre Dedieu, Gregorio Malajovich
We give an upper bound in O(d ^((n+1)/2)) for the number of critical points of a normal random polynomial with degree d and at most n variables. Using the large deviation principle…
On the Curvature of the Central Path of Linear Programming Theory
Jean-Pierre Dedieu, Gregorio Malajovich, Mike Shub
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 i…
Newton Method on Riemannian Manifolds: Covariant Alpha-Theory
Jean-Pierre Dedieu, Pierre Priouret, Gregorio Malajovich
In this paper we study quantitative aspects of Newton method for finding zeros of mappings f: M_n -> R^n and vector fields X: M_x -> TM_n