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On solving block-structured indefinite linear systems
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DOI：10.1137/S1064827500375096.png)
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Abstract
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We consider 2 x 2 block indefinite linear systems whose (2, 2) block is zero. Such systems arise in many applications. We discuss two techniques that are based on modifying the ( 1, 1) block in a way that makes the system easier to solve. The main part of the paper focuses on an augmented Lagrangian approach: a technique that modifies the ( 1,1) block without changing the system size. The choice of the parameter involved, the spectrum of the linear system, and its condition number are discussed, and some analytical observations are provided. A technique of deflating the ( 1,1) block is then introduced. Finally, numerical experiments that validate the analysis are presented.
Keywords:
indefinite linear systems
condition number
Schur complement
singularity
spectrum
augmented Lagrangian
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