On the Algebraic Properties of Intervals and Some Applications

On the Algebraic Properties of Intervals and Some Applications The algebraic properties of interval vectors (boxes) are studied. Quasilinear spaces with group structure are studied. Some fundamental algebraic properties are developed, especially in relation to the quasidistributive law, leading to a generalization of the familiar theory of linear spaces. In particular, linear dependence and basis are defined. It is proved that a quasilinear space with group structure is a direct sum of a linear and a symmetric space. A detailed characterization of symmetric quasilinear spaces with group structure is found. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Reliable Computing Springer Journals

On the Algebraic Properties of Intervals and Some Applications

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Publisher
Kluwer Academic Publishers
Copyright
Copyright © 2001 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:1011418014248
Publisher site
See Article on Publisher Site

Abstract

The algebraic properties of interval vectors (boxes) are studied. Quasilinear spaces with group structure are studied. Some fundamental algebraic properties are developed, especially in relation to the quasidistributive law, leading to a generalization of the familiar theory of linear spaces. In particular, linear dependence and basis are defined. It is proved that a quasilinear space with group structure is a direct sum of a linear and a symmetric space. A detailed characterization of symmetric quasilinear spaces with group structure is found.

Journal

Reliable ComputingSpringer Journals

Published: Oct 3, 2004

References

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