Summary: Math. Nachr. 192 (1998), 23-36
The Shape of the Solution Set for Systems of Interval Linear
Equations with Dependent Coefficients
By GÖTZ ALEFELD of Karlsruhe, VLADIK KREINOVICHof EI Paso, and
GÜNTER MAYER of Rostock
(Received October 20, 1995)
(Revised Version March 22, 1996)
Abstract. A standard system of interval linear equations is defined by Ax = b, where A is
an m x n eoeffieientmatrix with (compact) intervals as entries, and b is an m- dimensional veetor
whose eomponents are eompaet intervals. It is known that for systems of intervallinear equations the
solution set, i. e., the set of all veetors x for whieh Ax =b for some A E A and bEb, is a polyhedron.
In some eases, it makes sense to eonsider not all possible A E A and bEb, but only those A and b
that satisfy eertain linear eonditions deseribing dependeneies between the eoefficients. For example,
if we allow only symmetrie matrices A (aij = aji)' then the corresponding solution set beeomes (in
general) pieeewise - quadratie.
In this paper, we show that for general dependeneies, we ean have arbitrary (semi)algebraie sets as
projeetions of solution sets.
1. Informal Introduction
Many real-life problems require solution of the systems of linear equations Ax =b,