Diagrammatic Analysis of Interval Linear Equations - Part II: The Two-Dimensional Case and Generalization to n Dimensions

Diagrammatic Analysis of Interval Linear Equations - Part II: The Two-Dimensional Case and... Using the results obtained for the one-dimensional case in Part I (Reliable Computing 9(1) (2003), pp. 1–20) of the paper, an analysis of the two-dimensional relational expression a 1 ⋅ x 1 + a 2 ⋅ x 2 ◊ b, where ◊ ε {≖, ⫆, ⫅, =}, is conducted with the help of a midpoint-radius diagram and other auxiliary diagrams. The solution sets are obtained with a simple boundary-line selection rule derived using these tools, and are characterized by types of one-dimensional cuts through the solution space. A classification of basic possible solution types is provided in detail. The generalization of the approach for n-dimensional interval systems and avenues for further research are also outlined. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Reliable Computing Springer Journals

Diagrammatic Analysis of Interval Linear Equations - Part II: The Two-Dimensional Case and Generalization to n Dimensions

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Publisher
Springer Journals
Copyright
Copyright © 2003 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:1024603432484
Publisher site
See Article on Publisher Site

Abstract

Using the results obtained for the one-dimensional case in Part I (Reliable Computing 9(1) (2003), pp. 1–20) of the paper, an analysis of the two-dimensional relational expression a 1 ⋅ x 1 + a 2 ⋅ x 2 ◊ b, where ◊ ε {≖, ⫆, ⫅, =}, is conducted with the help of a midpoint-radius diagram and other auxiliary diagrams. The solution sets are obtained with a simple boundary-line selection rule derived using these tools, and are characterized by types of one-dimensional cuts through the solution space. A classification of basic possible solution types is provided in detail. The generalization of the approach for n-dimensional interval systems and avenues for further research are also outlined.

Journal

Reliable ComputingSpringer Journals

Published: Oct 17, 2004

References

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