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 …

The classical (Turing) theory of computation has been extraordinarily successful in providing
the foundations and framework for theoretical computer science. Yet its dependence on 0s …

We consider the local sensitivity of least-squares formulations of inverse problems. The sets
of inputs and outputs of these problems are assumed to have the structures of Riemannian …

The modern theory of condition measures for convex optimization problems was initially
developed for convex problems in the conic format (CP_d)\qquad\z_*:=\min_x{c^tx|Ax …

We describe and analyze a numerical algorithm for computing the homology (Betti numbers
and torsion coefficients) of real projective varieties. Here numerical means that the algorithm …

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

We analyze the probability that a random m-dimensional linear subspace of R^n both
intersects a regular closed convex cone C⊆R^n and lies within distance α of an m …

Considering mean-variance portfolio problems with uncertain model parameters, we
contrast the classical absolute robust optimization approach with the relative robust …

In recent decades, condition numbers have joined forces with probabilistic analysis to give
rise to a form of condition-based analysis of algorithms. In this paper we survey how this …

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 …