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 …

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 …

In a recent paper (Cucker et al., 2008 [8]) we analyzed a numerical algorithm for computing
the number of real zeros of a polynomial system. The analysis relied on a condition number …

This paper has two agendas. Firstly, we exhibit new results for coverage processes. Let p (n,
m, α) be the probability that n spherical caps of angular radius α in S m do not cover the …

We perform a smoothed analysis of Renegar's condition number for linear programming by
analyzing the distribution of the distance to ill-posedness of a linear program subject to a …

Let A:Y→X be a linear map and K⊆X be a regular closed convex cone. Consider the
problem of finding a nontrivial solution to the conic feasibility problem Ay∈K. Condition …

We present some recent results on the probabilistic behaviour of interior point methods for
the convex conic feasibility problem and for homotopy methods solving complex polynomial …

We perform a smoothed analysis of the GCC-condition number C (A) of the linear
programming feasibility problem ∃ x ∈ R^ m+ 1\, Ax< 0. Suppose that ̄ A is any matrix with …

We consider the conic feasibility problem associated with the linear homogeneous system
Ax≤ 0, x≠ 0. The complexity of iterative algorithms for solving this problem depends on a …

We consider the conic feasibility problem associated with linear homogeneous systems of
inequalities. The complexity of iterative algorithms for solving this problem depends on a …