Vavasis, Stephen A.2007-04-232007-04-231992-04http://techreports.library.cornell.edu:8081/Dienst/UI/1.0/Display/cul.cs/TR92-1280https://hdl.handle.net/1813/7120An equilibrium system (also known as a KKT system, a saddlepoint system or a sparse tableau) is a square linear system with a certain structure. G. Strang has observed that equilibrium systems arise in optimization, finite elements, structural analysis and electrical networks. Recently, G. W. Stewart established a norm bound for a type of equilibrium system in the case that the "stiffness" portion of the system is very ill-conditioned. In this paper, we investigate the algorithmic implications of Stewart's result. We show that all standard textbook algorithms for equilibrium systems are unstable. Then we show that a certain hybrid method has the right stability property.2671745 bytes506966 bytesapplication/pdfapplication/postscripten-UScomputer sciencetechnical reporttechnical report