Zobrazeno 1 - 10
of 92
pro vyhledávání: '"MALAJOVICH, GREGORIO"'
Autor:
Malajovich, Gregorio
The expected number of real projective roots of orthogonally invariant random homogeneous real polynomial systems is known to be equal to the square root of the B\'ezout number. A similar result is known for random multi-homogeneous systems, invarian
Externí odkaz:
http://arxiv.org/abs/2204.06081
Autor:
Malajovich, Gregorio
Renormalized homotopy continuation on toric varieties is introduced as a tool for solving sparse systems of polynomial equations, or sparse systems of exponential sums. The cost of continuation depends on a renormalized condition length, defined as a
Externí odkaz:
http://arxiv.org/abs/2005.01223
Autor:
Malajovich, Gregorio, Shub, Mike
Publikováno v:
Journal of the ACM 66(4) Article 27 pp 1-38 (May 2019)
We develop a complexity theory for approximate real computations. We first produce a theory for exact computations but with condition numbers. The input size depends on a condition number, which is not assumed known by the machine. The theory admits
Externí odkaz:
http://arxiv.org/abs/1803.03600
Autor:
Malajovich, Gregorio
Publikováno v:
Foundations of Computational Mathematics 19(1) 1-53 (2019)
This paper investigates the cost of solving systems of sparse polynomial equations by homotopy continuation. First, a space of systems of $n$-variate polynomial equations is specified through $n$ monomial bases. The natural locus for the roots of tho
Externí odkaz:
http://arxiv.org/abs/1606.03410
Autor:
Malajovich, Gregorio
Publikováno v:
Foundations of Computational Mathematics (2017) 17(5) 1293-1334
The mixed volume counts the roots of generic sparse polynomial systems. Mixed cells are used to provide starting systems for homotopy algorithms that can find all those roots, and track no unnecessary path. Up to now, algorithms for that task were of
Externí odkaz:
http://arxiv.org/abs/1412.0480
Autor:
Malajovich, Gregorio
The average mixed volume of a random projection of $d$ convex bodies in $\mathbb R^n$ is bounded above in terms of a quermassintegral.
Externí odkaz:
http://arxiv.org/abs/1410.5756
Autor:
MALAJOVICH, GREGORIO1 gregorio.malajovich@gmail.com, SHUB, MIKE2 mshub@ccny.cuny.edu
Publikováno v:
Journal of the ACM. Aug2019, Vol. 66 Issue 4, p1-38. 38p.
Autor:
Malajovich, Gregorio
Those lectures revolve around the following problem: given a system of n real polynomials in n variables, count the number of real roots. The first lecture is a course on Newton iteration and alpha-theory. The second describes an inclusion-exclusion
Externí odkaz:
http://arxiv.org/abs/1211.2120
Autor:
Malajovich, Gregorio
Publikováno v:
Foundations of Computational Mathematics 13(6) pp 867-884 (dec. 2013)
This paper investigates the expected number of complex roots of nonlinear equations. Those equations are assumed to be analytic, and to belong to certain inner product spaces. Those spaces are then endowed with the Gaussian probability distribution.
Externí odkaz:
http://arxiv.org/abs/1106.6014
Publikováno v:
IMA Journal of Numerical Analysis 2012
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 choose the step size for a Newton based homotopy method so that we approxim
Externí odkaz:
http://arxiv.org/abs/1104.2084