# A Method for Outer Interval Solution of Systems of Linear Equations Depending Linearly on Interval Parameters

A Method for Outer Interval Solution of Systems of Linear Equations Depending Linearly on... Consider the systems of linear interval equations whose coefficients are linear functions of interval parameters. Such systems, called parametrized systems of linear interval equations, are encountered in many practical problems, e.g in electrical engineering and structure mechanics. A direct method for computing a tight enclosure for the solution set is proposed in this paper. It is proved that for systems with real matrix and interval right-hand vector the method generates the hull of the solution set. For such systems an explicit formula for the hull is also given. Finally some numerical examples are provided to demonstrate the usefulness of the method in structure mechanics. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Reliable Computing Springer Journals

# A Method for Outer Interval Solution of Systems of Linear Equations Depending Linearly on Interval Parameters

, Volume 12 (2) – Jan 1, 2006
14 pages

/lp/springer_journal/a-method-for-outer-interval-solution-of-systems-of-linear-equations-isvtZEczyN
Publisher
Springer Journals
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.
10.1007/s11155-006-4878-y
Publisher site
See Article on Publisher Site

### Abstract

Consider the systems of linear interval equations whose coefficients are linear functions of interval parameters. Such systems, called parametrized systems of linear interval equations, are encountered in many practical problems, e.g in electrical engineering and structure mechanics. A direct method for computing a tight enclosure for the solution set is proposed in this paper. It is proved that for systems with real matrix and interval right-hand vector the method generates the hull of the solution set. For such systems an explicit formula for the hull is also given. Finally some numerical examples are provided to demonstrate the usefulness of the method in structure mechanics.

### Journal

Reliable ComputingSpringer Journals

Published: Jan 1, 2006

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