Summary: Computing [Suppl] 16, 1-22 (2002)
@ Springer-Verlag 2002
Printed in Austria
On Symmetrie Solution Sets
G. Alefeld,V. Kreinovichand G. Mayer
Given an n x n interval matrix [,4]and an interval vector [b]with n components we present an overview
on existing results on the solution set Ssym of linear systems of equations Ax = b with symmetrie
matrices A E (A]and veetors b E [b].Similarly we eonsider the set Esymof eigenpairs associated with the
symmetrie matrices A E [A].We report on characterizations of Ssymby means of inequalities, by means
of interseetion of sets, and by an approach which is generalizable to more general dependencies of the
en'tries. We also reeall two methods for enclosing Ssymby means of interval veetors, and we mention a
charaeterization of Esym.
AMS Subject Classifications: 65GIO.
Keywords: Solution set of linear systems, symmetrie solution set of linear systems, eigenpair set,
symmetrie eigenpair set, linear interval systems, Oettli-Prager theorem.
With this paper we intend to give an overview on existing results for the sym-
metric solution set