[BOOK][B] Condition: The geometry of numerical algorithms
P Bürgisser, F Cucker - 2013 - books.google.com
This book gathers threads that have evolved across different mathematical disciplines into
seamless narrative. It deals with condition as a main aspect in the understanding of the …
seamless narrative. It deals with condition as a main aspect in the understanding of the …
Turning intractable counting into sampling: Computing the configurational entropy of three-dimensional jammed packings
We present a numerical calculation of the total number of disordered jammed configurations
Ω of N repulsive, three-dimensional spheres in a fixed volume V. To make these calculations …
Ω of N repulsive, three-dimensional spheres in a fixed volume V. To make these calculations …
Zero distribution of random sparse polynomials
T Bayraktar - Michigan Mathematical Journal, 2017 - projecteuclid.org
We study the asymptotic zero distribution of random Laurent polynomials whose supports
are contained in dilates of a fixed integral polytope P as their degree grow. We consider a …
are contained in dilates of a fixed integral polytope P as their degree grow. We consider a …
On the number of real zeros of random fewnomials
Consider a system f_1(x)=0,...,f_n(x)=0 of n random real polynomial equations in n variables,
where each f_i has a prescribed set of exponent vectors described by a set A⊆N^n of …
where each f_i has a prescribed set of exponent vectors described by a set A⊆N^n of …
Deformation techniques for sparse systems
G Jeronimo, G Matera, P Solerno… - Foundations of …, 2009 - Springer
We exhibit a probabilistic symbolic algorithm for solving zero-dimensional sparse systems.
Our algorithm combines a symbolic homotopy procedure, based on a flat deformation of a …
Our algorithm combines a symbolic homotopy procedure, based on a flat deformation of a …
Computing mixed volume and all mixed cells in quermassintegral time
G Malajovich - Foundations of Computational Mathematics, 2017 - Springer
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 …
used to provide starting systems for homotopy algorithms that can find all those roots and …
Polyhedral homotopies in Cox coordinates
We introduce the Cox homotopy algorithm for solving a sparse system of polynomial
equations on a compact toric variety X Σ. The algorithm lends its name from a construction …
equations on a compact toric variety X Σ. The algorithm lends its name from a construction …
On the curvature of the central path of linear programming theory
JP Dedieu, G Malajovich, M Shub - Foundations of Computational …, 2005 - Springer
FOUNDATIONSOF COMPUTATIONAL MATHEMATICS Page 1 © 2005 SFoCM DOI:
10.1007/s10208-003-0116-8 Found. Comput. Math. 145–171 (2005) The Journal of the Society for …
10.1007/s10208-003-0116-8 Found. Comput. Math. 145–171 (2005) The Journal of the Society for …
Condition numbers for the cube. i: Univariate polynomials and hypersurfaces
J Tonelli-Cueto, E Tsigaridas - … of the 45th International Symposium on …, 2020 - dl.acm.org
The condition-based complexity analysis framework is one of the gems of modern numerical
algebraic geometry and theoretical computer science. One of the challenges that it poses is …
algebraic geometry and theoretical computer science. One of the challenges that it poses is …
Average Euler characteristic of random real algebraic varieties
P Bürgisser - Comptes Rendus Mathematique, 2007 - Elsevier
We determine the expected curvature polynomial of real projective varieties given as the
zero set of independent random polynomials with Gaussian distribution, which is invariant …
zero set of independent random polynomials with Gaussian distribution, which is invariant …