Summary: SIAM J. MATRIX ANAL. ApPL.
Vol. 18, No. 3, pp. 693-705, July 1997
@ 1997 Society for Industrial and Applied Mathematics
ON THE SHAPE OF THE SYMMETRIC, PERSYMMETRlC, AND
SKEW-SYMMETRlC 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 skew-symmetrie 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, skew-symmetrie matriees, Oettli-Prager theorem,
Fourier-Motzkin elimination, interval analysis
AMS subject classifications. 65GlO,65F05
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-