Diagrammatic representation for interval arithmetic
The paper presents a diagrammatic representation of a standard interval space (the so-called “MR-diagram”), and shows how to represent and perform interval arithmetic and derive its various properties using the diagram. The representation is an extension and refinement of the IS-diagram representati...
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| Published in | Linear algebra and its applications Vol. 324; no. 1; pp. 55 - 80 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Inc
15.02.2001
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| Abstract | The paper presents a diagrammatic representation of a standard interval space (the so-called “MR-diagram”), and shows how to represent and perform interval arithmetic and derive its various properties using the diagram. The representation is an extension and refinement of the IS-diagram representation devised earlier by the author to represent interval relations. First, the MR-diagram is defined together with appropriate graphical notions and constructions for basic interval relations and operations. Second, diagrammatic constructions for all standard arithmetic operations are presented. Several examples of the use of these constructions to aid reasoning about various simple, though nontrivial, properties of interval arithmetic are included in order to show how the representation facilitates both deeper understanding of the subject matter and reasoning about its properties. |
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| AbstractList | The paper presents a diagrammatic representation of a standard interval space (the so-called “MR-diagram”), and shows how to represent and perform interval arithmetic and derive its various properties using the diagram. The representation is an extension and refinement of the IS-diagram representation devised earlier by the author to represent interval relations. First, the MR-diagram is defined together with appropriate graphical notions and constructions for basic interval relations and operations. Second, diagrammatic constructions for all standard arithmetic operations are presented. Several examples of the use of these constructions to aid reasoning about various simple, though nontrivial, properties of interval arithmetic are included in order to show how the representation facilitates both deeper understanding of the subject matter and reasoning about its properties. |
| Author | Kulpa, Zenon |
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| Cites_doi | 10.1023/A:1008323427489 10.1111/j.1551-6708.1987.tb00863.x 10.1007/978-1-4615-2025-2_14 10.1007/978-3-7091-8577-3_3 10.2514/2.164 10.1016/S0952-1976(98)00067-0 10.1016/0165-0114(90)90204-J 10.1006/jvlc.1993.1020 10.1145/182.358434 10.1016/0004-3702(92)90090-K 10.1007/3-540-07170-9_23 10.1007/3-540-54316-3 10.1007/BF02388185 10.1007/BF02281714 10.1023/A:1009919304728 |
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| Keywords | Interval space 65G40 51M15 Geometric interpretation 00A35 Diagrammatic representation Interval arithmetic Diagrammatic reasoning |
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| Snippet | The paper presents a diagrammatic representation of a standard interval space (the so-called “MR-diagram”), and shows how to represent and perform interval... |
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| SubjectTerms | Diagrammatic reasoning Diagrammatic representation Geometric interpretation Interval arithmetic Interval space |
| Title | Diagrammatic representation for interval arithmetic |
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