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- 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)

- Felipe Cucker, Teresa Krick, Gregorio Malajovich, Mario Wschebor
- ArXiv
- 2009

We show a Condition Number Theorem for the condition number of zero counting for real polynomial systems. That is, we show that this condition number equals the inverse of the normalized distance toâ€¦ (More)

- Gregorio Malajovich
- Foundations of Computational Mathematics
- 2017

V (A1, . . . ,An) def = 1 n! âˆ‚ âˆ‚t1âˆ‚t2 Â· Â· Â· âˆ‚tn Vol(t1A1 + Â· Â· Â·+ tnAn) where t1, . . . , tn â‰¥ 0 and the derivative is taken at t = 0. The normalization factor 1/n! ensures that V (A, . . . ,A) =â€¦ (More)

- Felipe Cucker, Teresa Krick, Gregorio Malajovich, Mario Wschebor
- J. Complexity
- 2008

We describe an algorithm to count the number of distinct real zeros of a polynomial (square) system f . The algorithm performs O(log(nDÎº(f))) iterations (grid refinements) where n is the number ofâ€¦ (More)

- Gregorio Malajovich, Maurice Rojas
- Theor. Comput. Sci.
- 2004

Let F :=(f1, . . . , fn) be a random polynomial system with fixed n-tuple of supports. Our main result is an upper bound on the probability that the condition number of f in a region U is larger thanâ€¦ (More)

- Felipe Cucker, Teresa Krick, Gregorio Malajovich, Mario Wschebor
- ArXiv
- 2008

In a recent paper [7] we analyzed a numerical algorithm for computing the number of real zeros of a polynomial system. The analysis relied on a condition number Îº(f) for the input system f . In thisâ€¦ (More)

Abstract Let f :=(f1, . . . , fn) be a sparse random polynomial system. This means that each f i has fixed support (list of possibly non-zero coefficients) and each coefficient has a Gaussianâ€¦ (More)

- Gregorio Malajovich
- J. Complexity
- 2001

A model of computation is defined over the algebraic numbers and over number fields. This model is non-uniform, and the cost of operations depends on the height of the operands and on the degree ofâ€¦ (More)

A new algorithm for splitting polynomials is presented. This algorithm requires O(d log âˆ’1)1+Î´ floating point operations, with O(log âˆ’1)1+Î´ bits of precision. As far as complexity is concerned, thisâ€¦ (More)

- Jean-Pierre Dedieu, Gregorio Malajovich
- J. Complexity
- 2008

We give an upper bound in O(d) for the number of critical points of a normal random polynomial. The number of minima (resp. maxima) is in O(d)Pn, where Pn is the (unknown) measure of the set ofâ€¦ (More)