34 citations · 108 across the 17 of their papers we have counts for
7 papers · 1 filter
Wilkinson's bus: Weak condition numbers, with an application to singular polynomial eigenproblems
Martin Lotz, Vanni Noferini
We propose a new approach to the theory of conditioning for numerical analysis problems for which both classical and stochastic perturbation theory fail to predict the observed acc…
Effective Condition Number Bounds for Convex Regularization
Dennis Amelunxen, Martin Lotz, Jake Walvin
We derive bounds relating Renegar's condition number to quantities that govern the statistical performance of convex regularization in settings that include the -analysis s…
Average-case complexity without the black swans
Dennis Amelunxen, Martin Lotz
We introduce the concept of weak average-case analysis as an attempt to achieve theoretical complexity results that are closer to practical experience than those resulting from tra…
On the volume of tubular neighborhoods of real algebraic varieties
Martin Lotz
The problem of determining the volume of a tubular neighbourhood has a long and rich history. Bounds on the volume of neighbourhoods of algebraic sets have turned out to play an im…
Adversarial Smoothed Analysis
Felipe Cucker, Raphael Hauser, Martin Lotz
The purpose of this note is to extend the results on uniform smoothed analysis of condition numbers from \cite{BuCuLo:07} to the case where the perturbation follows a radially symm…
The probability that a small perturbation of a numerical analysis problem is difficult
Peter Buergisser, Felipe Cucker, Martin Lotz
We prove a general theorem providing smoothed analysis estimates for conic condition numbers of problems of numerical analysis. Our probability estimates depend only on geometric i…