Some Remarks on the Generalised Bareiss and Levinson Algorithms

The Bareiss (or Schur) and Levinson algorithms are the most popular algorithms for solving linear systems with dense n × n Toeplitz coefficient matrix in O(n 2) arithmetic operations. Both algorithms have been generalised to solve linear systems whose n × n coefficient matrices A are not necessarily Toeplitz (in O(n 3) operations). We show in this paper that the generalised Levinson algorithm is a direct consequence of the generalised Bareiss algorithm, thereby considerably simplifying its presentation in comparison to previous work.

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