We consider 2 ×2 block inde finite 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 modi fies 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 de flating the (1,1)block is then introduced.Finally,numerical experiments that validate the analysis are presented.
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Golub et al. (2003) studied this question.
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