Qualitative Properties of the Conjugate Gradient and Lanczos Methods in a Matrix Framework

@inproceedings{Eijkhout1992QualitativePO,
  title={Qualitative Properties of the Conjugate Gradient and Lanczos Methods in a Matrix Framework},
  author={Victor Eijkhout},
  year={1992}
}
This paper presents the conjugate gradient and Lanczos methods in a matrix framework, focusing mostly on orthogonality properties of the various vector sequences generated. Various aspects of the methods, such as choice of inner product, preconditioning, and relations to other iterative methods will be considered. Minimization properties of the methods and the fact that they can compute successive approximations to the solution of a linear system will be proved as corollary.