Approximate Inverse Circulant-plus-Diagonal Preconditioners for Toeplitz-plus-Diagonal Matrices

@article{Ng2010ApproximateIC,
  title={Approximate Inverse Circulant-plus-Diagonal Preconditioners for Toeplitz-plus-Diagonal Matrices},
  author={Michael K. Ng and Jianyu Pan},
  journal={SIAM J. Scientific Computing},
  year={2010},
  volume={32},
  pages={1442-1464}
}
We consider the solutions of Hermitian positive definite Toeplitz-plus-diagonal systems $(T+D)x=b$, where $T$ is a Toeplitz matrix and $D$ is diagonal and positive. However, unlike the case of Toeplitz systems, no fast direct solvers have been developed for solving them. In this paper, we employ the preconditioned conjugate gradient method with approximate inverse circulant-plus-diagonal preconditioners to solving such systems. The proposed preconditioner can be constructed and implemented… CONTINUE READING

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