Superfast solution of Toeplitz systems based on syzygy reduction
Symbolic Computation
2013-01-25 v1 Numerical Analysis
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.
Keywords
Cite
@article{arxiv.1301.5798,
title = {Superfast solution of Toeplitz systems based on syzygy reduction},
author = {Houssam Khalil and Bernard Mourrain and Michelle Schatzman},
journal= {arXiv preprint arXiv:1301.5798},
year = {2013}
}
Comments
(07/11/2011). arXiv admin note: substantial text overlap with arXiv:0903.1244