Average-Case Perturbations and Smooth Condition Numbers

TL;DR

This paper introduces a new condition number tailored for directionally uniform perturbations, relating it to classical condition numbers and exploring its applications across various problems.

Contribution

It proposes a novel condition number for directional perturbations and analyzes its relation to classical measures, broadening the scope of condition number analysis.

Findings

New condition number for directional perturbations

Relation established with classical condition numbers

Application to diverse problem classes

Abstract

We define a new condition number adapted to directionally uniform perturbations. The definitions and theorems can be applied to a large class of problems. We show the relation with the classical condition number, and study some interesting examples.