An equilibrium system (also known as a Karush-Kuhn-Tucker (KKT) system
, a saddlepoint system, or a sparse tableau) is a square linear system
with a certain structure. Strang [SIAM Rev., 30 (1988), pp. 283-297]
has observed that equilibrium systems arise in optimization, finite el
ements, structural analysis, and electrical networks. Recently, Stewar
t [Linear Algebra Appl., 112 (1989), pp. 189-193] established a norm b
ound for a type of equilibrium system in the case when the ''stiffness
'' portion of the system is very ill-conditioned. This paper investiga
tes the algorithmic implications of Stewart's result. It is shown that
several algorithms for equilibrium systems appearing in applications
textbooks are unstable. A certain hybrid method is then proposed, and
it is proved that the new method has the right stability property.