Summary
This paper presents a new algorithm for computing theQR factorization of anm×n Toeplitz matrix inO(mn) operations. The algorithm exploits the procedure for the rank-1 modification and the fact that both principal (m−1)×(n−1) submatrices of the Toeplitz matrix are identical. An efficient parallel implementation of the algorithm is possible.
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Bojanczyk, A.W., Brent, R.P. & de Hoog, F.R. QR factorization of Toeplitz matrices. Numer. Math. 49, 81–94 (1986). https://doi.org/10.1007/BF01389431
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DOI: https://doi.org/10.1007/BF01389431