# Diagrammatic Analysis of Interval Linear Equations - Part I: Basic Notions and the One-Dimensional Case

Diagrammatic Analysis of Interval Linear Equations - Part I: Basic Notions and the... Different solution sets for the interval linear system A ⋅ x = b are characterized and classified using diagrammatic tools for interval analysis developed recently. In Part I, a thorough analysis of the basic, one-dimensional expression a ⋅ x ◊ b is conducted, with the help of an appropriate interval space diagram, in which all the needed relations ◊ ε{ ≖, \$\$\supseteq\$\$ , \$\$\subseteq\$\$ , = } are directly representable. The solution sets are obtained with simple diagrammatic constructions, and are characterized by quotient sequences of a and b. A complete classification of all possible solution types is developed in this way, with various ways of visualizing the structure of the set of these types. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Reliable Computing Springer Journals

# Diagrammatic Analysis of Interval Linear Equations - Part I: Basic Notions and the One-Dimensional Case

Reliable Computing, Volume 9 (1) – Oct 17, 2004
20 pages

/lp/springer_journal/diagrammatic-analysis-of-interval-linear-equations-part-i-basic-Z8lSuyq07C
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.
10.1023/A:1023022826879
Publisher site
See Article on Publisher Site

### Abstract

Different solution sets for the interval linear system A ⋅ x = b are characterized and classified using diagrammatic tools for interval analysis developed recently. In Part I, a thorough analysis of the basic, one-dimensional expression a ⋅ x ◊ b is conducted, with the help of an appropriate interval space diagram, in which all the needed relations ◊ ε{ ≖, \$\$\supseteq\$\$ , \$\$\subseteq\$\$ , = } are directly representable. The solution sets are obtained with simple diagrammatic constructions, and are characterized by quotient sequences of a and b. A complete classification of all possible solution types is developed in this way, with various ways of visualizing the structure of the set of these types.

### Journal

Reliable ComputingSpringer Journals

Published: Oct 17, 2004

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