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Average-case complexity without the black swans
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Amelunxen, D. and Lotz, Martin (2017) Average-case complexity without the black swans. Journal of Complexity, 41 . pp. 82-101. doi:10.1016/j.jco.2016.12.002
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Official URL: https://doi.org/10.1016/j.jco.2016.12.002
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, Engineering and Medicine > 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: |
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| Volume: | 41 | ||||||||
| Page Range: | pp. 82-101 | ||||||||
| DOI: | 10.1016/j.jco.2016.12.002 | ||||||||
| Status: | Peer Reviewed | ||||||||
| Publication Status: | Published | ||||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||||
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