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arXiv · 1301.5798

Superfast solution of Toeplitz systems based on syzygy reduction

Houssam Khalil·Bernard Mourrain·Michelle Schatzman
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Abstract

We present a new superfast algorithm for solving Toeplitz systems. This algorithm is based on a relation between the solution of such problems and syzygies of polynomials or moving lines. We show an explicit connection between the generators of a Toeplitz matrix and the generators of the corresponding module of syzygies. We show that this module is generated by two elements and the solution of a Toeplitz system T u=g can be reinterpreted as the remainder of a vector depending on g, by these two generators. We obtain these generators and this remainder with computational complexity O(n log^2 n) for a Toeplitz matrix of size nxn.

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Houssam Khalil, Bernard Mourrain, Michelle Schatzman. 2013-01-24. Superfast solution of Toeplitz systems based on syzygy reduction. https://arxiv.org/abs/1301.5798

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