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# Calculation of exact bounds for the solution set of linear interval systems

Publikationstyp

Journal Article

Publikationsdatum

1997-01-15

Sprache

English

Author

Institut

TORE-URI

Enthalten in

Volume

251

Start Page

321

End Page

340

Citation

Linear Algebra and Its Applications 251: 321-340 (1997-01-15)

Publisher DOI

Scopus ID

Publisher

American Elsevier Publ.

This paper presents some topological and graph theoretical properties of the solution set of linear algebraic systems with interval coefficients. Based on these properties, we describe a method which, in a finite number of steps, either calculates exact bounds for each component of the solution set, or finds a singular matrix within the interval coefficients. The calculation of exact bounds of the solution set is known to be NP-hard. Our method needs p calls of a polynomial-time algorithm, where p is the number of nonempty intersections of the solution set with the orthants. Frequently, due to physical or economical requirements, many variables do not change the sign. In those cases p is small, and our method works efficiently. © Elsevier Science Inc., 1997.