Complexity of Some Linear Problems with Interval Data

Complexity of Some Linear Problems with Interval Data During the recent years, a number of linear problems with interval data have been proved to be NP-hard. These results may seem rather obscure as regards the ways in which they were obtained. This survey paper is aimed at demonstrating that in fact it is not so, since many of these results follow easily from the recently established fact that for the subordinate matrix norm ‖ · ‖∞,1 it is NP-hard to decide whether ‖A‖∞,1 ≥ 1 holds, even in the class of symmetric positive definite rational matrices. After a brief introduction into the basic topics of the complexity theory in Section 1 and formulation of the underlying norm complexity result in Section 2, we present NP-hardness results for checking properties of interval matrices (Section 3), computing enclosures (Section 4), solvability of rectangular linear interval systems (Section 5), and linear and quadratic programming (Section 6). Due to space limitations, proofs are mostly only ketched to reveal the unifying role of the norm complexity result; technical details are omitted. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Reliable Computing Springer Journals

Complexity of Some Linear Problems with Interval Data

Loading next page...
 
/lp/springer_journal/complexity-of-some-linear-problems-with-interval-data-coSzihAJX2
Publisher
Kluwer Academic Publishers
Copyright
Copyright © 1997 by Kluwer Academic Publishers
Subject
Mathematics; Numeric Computing; Approximations and Expansions; Computational Mathematics and Numerical Analysis; Mathematical Modeling and Industrial Mathematics
ISSN
1385-3139
eISSN
1573-1340
D.O.I.
10.1023/A:1009987227018
Publisher site
See Article on Publisher Site

References

You’re reading a free preview. Subscribe to read the entire article.


DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 12 million articles from more than
10,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Unlimited reading

Read as many articles as you need. Full articles with original layout, charts and figures. Read online, from anywhere.

Stay up to date

Keep up with your field with Personalized Recommendations and Follow Journals to get automatic updates.

Organize your research

It’s easy to organize your research with our built-in tools.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

Monthly Plan

  • Read unlimited articles
  • Personalized recommendations
  • No expiration
  • Print 20 pages per month
  • 20% off on PDF purchases
  • Organize your research
  • Get updates on your journals and topic searches

$49/month

Start Free Trial

14-day Free Trial

Best Deal — 39% off

Annual Plan

  • All the features of the Professional Plan, but for 39% off!
  • Billed annually
  • No expiration
  • For the normal price of 10 articles elsewhere, you get one full year of unlimited access to articles.

$588

$360/year

billed annually
Start Free Trial

14-day Free Trial