Average-case complexity without the black swans

Research output: Contribution to journalArticle

  • Authors:
  • Martin Lotz
  • Dennis Amelunxen

Abstract

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 traditional approaches. The underlying paradigm is accepted in other areas such as non-asymptotic random matrix theory and compressive sensing, and has a particularly convincing interpretation in the most common situation encountered for condition numbers, where it amounts to replacing a null set of ill-posed inputs by a “numerical null set”. We illustrate the usefulness of these notions by considering three settings: (1) condition numbers that are inversely proportional to a distance of a homogeneous algebraic set of ill-posed inputs; (2) Renegar’s condition number for conic optimization; (3) the running time of power iteration for computing a leading eigenvector of a Hermitian matrix.

Bibliographical metadata

Original languageEnglish
Pages (from-to)82-101
JournalJournal of Complexity
Volume41
DOIs
StatePublished - 29 Dec 2016