 
Summary: SIAM J. MATRIX ANAL. ApPL.
Val. 16, No. 4, pp. 12231240, Oetober 1995
@ 1995 Society for lndustrial and Applied Mathematics
015
ON THE SYMMETRIC AND UNSYMMETRIC SOLUTION SET OF
INTER VAL SYSTEMS*
GÖTZ ALEFELDt AND GÜNTER MAYERt
Abstract. We eonsider the solution set S of real linear systems Ax = b with the n x n eoeffieient
matrix A varying between a lower bound A and an upper bound A, and with b similarly varying
between Q, b. First we list some properties on the shape of S if all matriees Aare nonsingular. Then
we restrict A to be nonsingular and symmetrie deriving a eomplete deseription for the boundary of
the eorresponding symmetrie solution set Ssym in the 2 x 2 ease. Finally we derive a new eriterion
for the feasibility of the Cholesky method with whieh bounds for Ssym ean be found.
Key words. linear interval equations, unsymmetrie solution set, enclosures far the solution
set of linear intervai systems, symmetrie linear systems, symmetrie solution set, interval Cholesky
method, eriteria of feasibility for the interval Cholesky method
AMS subject classifications. 65F05, 65G10
1. Introduction. In [2] we introdueed the interval Cholesky method in order to
find an interval enclosure [xjC of the symmetrie solution set
(1.1) Ssym := {x E Rnl Ax = b, A = AT E [A], bE [bJ},
