The Shape of the Solution Set for Systems of Interval Linear Equations with Dependent Coefficients

✍ Scribed by Götz Alefeld; Vladik Kreinovich; Günter Mayer

• Publisher: John Wiley and Sons
• Year: 1998
• Tongue: English
• Weight: 735 KB
• Volume: 192
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.19981920103

✦ Synopsis

A standard system of interval linear equations is defined by Ax = b, where A is an m x n coefficient matrix with (compact) intervals as entries, and b is an m-dimensional vector whose components are compact intervals. It is known that for systems of interval linear equations the solution set, i. e., the set of all vectors x for which Ax = b for some A E A and b E b, is a polyhedron.

In some cases, it makes sense to consider not all possible A E A and b E b, but only those A and b that satisfy certain linear conditions describing dependencies between the coefficients. For example, if we allow only symmetric matrices A (aij = aj;) , then the corresponding solution set becomes (in general) piecewisequadratic.

In this paper, we show that for general dependencies, we can have arbitrary (semi)algebraic sets as projections of solution sets.