Iterative Methods for Ill-conditioned Linear Systems from Optimization

@inproceedings{Gould1998IterativeMF,
  title={Iterative Methods for Ill-conditioned Linear Systems from Optimization},
  author={Nicholas I. M. Gould},
  year={1998}
}
Preconditioned conjugate-gradient methods are proposed for solving the ill-conditioned linear systems which arise in penalty and barrier methods for nonlinear minimization. The preconditioners are chosen so as to isolate the dominant cause of ill conditioning. The methods are stablized using a restricted form of iterative reenement. Numerical results illustrate the approaches considered. 
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