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Algorithms for structured linear systems solving and their implementation

Seung Gyu Hyun 1 Romain Lebreton 2 Éric Schost 1
2 ECO - Exact Computing
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
Abstract : There exists a vast literature dedicated to algorithms for structured matrices, but relatively few descriptions of actual implementations and their practical performance. In this paper, we consider the problem of solving Cauchy-like systems, and its application to mosaic Toeplitz systems, in two contexts: first in the unit cost model (which is a good model for computations over finite fields), then over Q. We introduce new variants of previous algorithms and describe an implementation of these techniques and its practical behavior. We pay a special attention to particular cases such as the computation of algebraic approximants.
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https://hal-lirmm.ccsd.cnrs.fr/lirmm-01484831
Contributor : Romain Lebreton <>
Submitted on : Tuesday, March 7, 2017 - 7:03:08 PM
Last modification on : Thursday, December 6, 2018 - 10:01:40 PM
Long-term archiving on: : Thursday, June 8, 2017 - 2:49:37 PM

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Seung Gyu Hyun, Romain Lebreton, Éric Schost. Algorithms for structured linear systems solving and their implementation. ISSAC: International Symposium on Symbolic and Algebraic Computation, Jul 2017, Kaiserslautern, Germany. pp.205-212, ⟨10.1145/3087604.3087659⟩. ⟨lirmm-01484831⟩

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