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Title: Stable Numerical Algorithms for Equilibrium Systems
Authors: Vavasis, Stephen A.
Keywords: computer science
technical report
Issue Date: Apr-1992
Publisher: Cornell University
Abstract: An 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.
Appears in Collections:Computer Science Technical Reports

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