A lookahead algorithm for the solution of block toeplitz systems

@article{Barel1997ALA,
  title={A lookahead algorithm for the solution of block toeplitz systems},
  author={Marc Van Barel and Adhemar Bultheel},
  journal={Linear Algebra and its Applications},
  year={1997},
  volume={266},
  pages={291-335}
}

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An extension of Levinson’s algorithm for solving linear systems with symmetric indefinite Toeplitz matrices is presented. This new algorithm is able to “look ahead” and, if necessary, use block
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An extension of the Bareiss algorithm to general Toeplitz systems is presented, and using look-ahead techniques, the proposed algorithm can skip over arbitrary blocks of singular or ill-conditioned submatrices, and at the same time, it still fully exploits the ToePlitz structure.
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This paper proposes a look-ahead scheme for such matrices and presents empirical results which demonstrate the improvement over the classical Schur algorithm for symmetric Toeplitz matrices with ill-conditioned principal minors.
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