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[An error in the catalogue corrected recently.]
This report contains a complete catalogue of all structural types
of the one-dimensional interval equation a · x = b.
The catalogue constitutes a basis for the analysis
of the general multidimensional case, as the configurations
of solution sets for the one-dimensional case describe
in full all possible radial cuts through the solution space
of the multidimensional interval equation.
To make the report self-contained, it first introduces
the basic notation for intervals and interval linear equations,
as well as diagrammatic tools needed for their analysis.
Then the analysis of the one-dimensional equation
is conducted, and a detailed catalogue of possible solution types
of such equations is provided, in both diagrammatic and tabular forms.
Finally, a short description of the computer program
(coded in Mathematica® 3.0)
implementing the type catalogue is included.
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upon
request. e-mail them to me.
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Interval analysis and computation