A New Technique in Systems Analysis Under Interval Uncertainty and Ambiguity

A New Technique in Systems Analysis Under Interval Uncertainty and Ambiguity The main subject of this work is mathematical and computational aspects of modeling of static systems under interval uncertainty and/or ambiguity. A cornerstone of the new approach we are advancing in the present paper is, first, the rigorous and consistent use of the logical quantifiers to characterize and distinguish different kinds of interval uncertainty that occur in the course of modeling, and, second, the systematic use of Kaucher complete interval arithmetic for the solution of problems that are minimax by their nature. As a formalization of the mathematical problem statement, concepts of generalized solution sets and AE-solution sets to an interval system of equations, inequalities, etc., are introduced. The major practical result of our paper is the development of a number of techniques for inner and outer estimation of the so-called AE-solution sets to interval systems of equations. We work out, among others, formal approach, generalized interval Gauss-Seidel iteration, generalized preconditioning and PPS-methods. Along with the general nonlinear case, the linear systems are treated more thoroughly. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Reliable Computing Springer Journals

A New Technique in Systems Analysis Under Interval Uncertainty and Ambiguity

Loading next page...
 
/lp/springer_journal/a-new-technique-in-systems-analysis-under-interval-uncertainty-and-i0BFNMqMHf
Publisher
Kluwer Academic Publishers
Copyright
Copyright © 2002 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:1020505620702
Publisher site
See Article on Publisher Site

Abstract

The main subject of this work is mathematical and computational aspects of modeling of static systems under interval uncertainty and/or ambiguity. A cornerstone of the new approach we are advancing in the present paper is, first, the rigorous and consistent use of the logical quantifiers to characterize and distinguish different kinds of interval uncertainty that occur in the course of modeling, and, second, the systematic use of Kaucher complete interval arithmetic for the solution of problems that are minimax by their nature. As a formalization of the mathematical problem statement, concepts of generalized solution sets and AE-solution sets to an interval system of equations, inequalities, etc., are introduced. The major practical result of our paper is the development of a number of techniques for inner and outer estimation of the so-called AE-solution sets to interval systems of equations. We work out, among others, formal approach, generalized interval Gauss-Seidel iteration, generalized preconditioning and PPS-methods. Along with the general nonlinear case, the linear systems are treated more thoroughly.

Journal

Reliable ComputingSpringer Journals

Published: Oct 13, 2004

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

DeepDyve Freelancer

DeepDyve Pro

Price
FREE
$49/month

$360/year
Save searches from
Google Scholar,
PubMed
Create lists to
organize your research
Export lists, citations
Read DeepDyve articles
Abstract access only
Unlimited access to over
18 million full-text articles
Print
20 pages/month
PDF Discount
20% off