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There are well-known fast algorithms, such as the Levinson recursion, for solving linear equations with a Toeplitz (or Hankel) coefficient matrix. This paper extends the saving obtained by the Levinson recursion for inversion of a Toeplitz matrix to problems involving the inversion of matrices which are the sum of Toeplitz and Hankel matrices.
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Merchant et al. (1982) studied this question.
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