# Symmetric inner-iteration preconditioning for rank-deficient least squares problems

@article{Morikuni2015SymmetricIP, title={Symmetric inner-iteration preconditioning for rank-deficient least squares problems}, author={K. Morikuni}, journal={arXiv: Numerical Analysis}, year={2015} }

Stationary iterative methods with a symmetric splitting matrix are performed as inner-iteration preconditioning for Krylov subspace methods. We give a necessary and sufficient condition such that the inner-iteration preconditioning matrix is definite, and show that conjugate gradient (CG) method preconditioned by the inner iterations determines a solution of a symmetric and positive semidefinite linear system, and the minimal residual (MR) method preconditioned by the inner iterations… Expand

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