Amelunxen, D. and Lot, Martin (2017) Average-case complexity without the black swans. Journal of Complexity, 41 . pp. 82-101.

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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.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Mathematics
Library of Congress Subject Headings (LCSH):	Hermitian operators, Conic sections , Numerical analysis, Probabilities
Journal or Publication Title:	Journal of Complexity
Publisher:	Academic Press
ISSN:	0885-064X
Official Date:	August 2017
Dates:	Date Event August 2017 Published 29 December 2016 Available 19 December 2016 Accepted
Date of first compliant deposit:	22 July 2019
Volume:	41
Page Range:	pp. 82-101
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access

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