 
Summary: SIAM J. MATRIX ANAL. ApPL.
Vol. 18, No. 3, pp. 693705, July 1997
@ 1997 Society for Industrial and Applied Mathematics
009
ON THE SHAPE OF THE SYMMETRIC, PERSYMMETRlC, AND
SKEWSYMMETRlC SOLUTION SET*
GÖTZ ALEFELDt, VLADIK KREINOVICH+, AND GÜNTER MAYER§
Dedicated to Prof. Dr. Gerhard Maeß, Rostock, on the occasion 01 his 60th birthday.
Abstract. We present a eharaeterization of the solution set S, the symmetrie solution set Ssyrn,
the persymmetrie solution set Sper, and the skewsymmetrie solution set Sskew of real linear systems
Ax = b with the n x n eoefficient matrix A varying between a lower bound A and an upper bound
A, and with b similarly varying between Q, b. We show that in eaeh orthant the sets Ssyrn, Sper,
and Sskew are, respectively, the intersection of S with sets, the boundaries of whieh are quadrics.
Key words. linear systems with perturbed input data, solution set of linear systems of equa
tions, symmetrie matriees, persymmetric matrices, skewsymmetrie matriees, OettliPrager theorem,
FourierMotzkin elimination, interval analysis
AMS subject classifications. 65GlO,65F05
PlI. 80895479896297069
L Introduction. Let [A] be an n x n matrix with eompact intervals as entries,
let [b]be a vector with n interval eomponents, and let E be the n x n permutation ma
