Polynomial Linear System Solving with Random Errors: new bounds and early termination technique

Autor: Eleonora, Guerrini, Romain, Lebreton, Ilaria, Zappatore

This paper deals with the polynomial linear system solving with errors (PLSwE) problem. Specifically, we focus on the evaluation-interpolation technique for solving polynomial linear systems and we assume that errors can occur in the evaluation step.

Externí odkaz: http://arxiv.org/abs/2102.04182

Polynomial Linear System Solving with Random Errors: new bounds and early termination technique

Autor: Eleonora Guerrini, Romain Lebreton, Ilaria Zappatore

Publikováno v: ISSAC 2021-46th International Symposium on Symbolic and Algebraic Computation
ISSAC 2021-46th International Symposium on Symbolic and Algebraic Computation, Jul 2021, Saint Petersburg, Russia. pp.171-178, ⟨10.1145/3452143.3465548⟩
ISSAC
International Symposium on Symbolic and Algebraic Computation (ISSAC 2021)
International Symposium on Symbolic and Algebraic Computation (ISSAC 2021), Jul 2021, Saint Petersburg, Russia. pp.171-178, ⟨10.1145/3452143.3465548⟩

This paper deals with the polynomial linear system solving with errors (PLSwE) problem. Specifically, we focus on the evaluation-interpolation technique for solving polynomial linear systems and we assume that errors can occur in the evaluation step.

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::8bf2ccd372db58503ed553789dcf890a

Simultaneous Conversions with the Residue Number System Using Linear Algebra

Autor: Pascal Giorgi, Éric Schost, Javad Doliskani, Romain Lebreton

Publikováno v: ACM Transactions on Mathematical Software
ACM Transactions on Mathematical Software, Association for Computing Machinery, 2018, 44 (3), pp.#27. ⟨10.1145/3145573⟩

International audience; We present an algorithm for simultaneous conversion between a given set of integers and their Residue Number System representations based on linear algebra. We provide a highly optimized implementation of the algorithm that ex

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::26e6f678c5f9d35ee9ed166c9d0f6ab2
https://doi.org/10.1145/3145573

Algorithms for structured linear systems solving and their implementation

Autor: Seung Gyu Hyun, Romain Lebreton, Éric Schost

Publikováno v: 42nd International Symposium on Symbolic and Algebraic Computation
ISSAC: International Symposium on Symbolic and Algebraic Computation
ISSAC: International Symposium on Symbolic and Algebraic Computation, Jul 2017, Kaiserslautern, Germany. pp.205-212, ⟨10.1145/3087604.3087659⟩
ISSAC

International audience; 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 Cauch

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::7dfbeae006e351ad25ab53f95b9684d9
https://hal-lirmm.ccsd.cnrs.fr/lirmm-01484831

Online order basis algorithm and its impact on the block Wiedemann algorithm

Autor: Pascal Giorgi, Romain Lebreton

Publikováno v: 39th International Symposium on Symbolic and Algebraic Computation
ISSAC: International Symposium on Symbolic and Algebraic Computation
ISSAC: International Symposium on Symbolic and Algebraic Computation, Jul 2014, Kobe, Japan. pp.202-209, ⟨10.1145/2608628.2608647⟩
ISSAC

International audience; Order bases are a fundamental tool for linear algebra with polynomial coefficients. In particular, block Wiedemann methods are nowadays able to tackle large sparse matrix problems because they benefit from fast order basis alg

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::117b934c43903286c6daf8ff9281aefb
https://hal-lirmm.ccsd.cnrs.fr/lirmm-01232873