Faster Algorithms for Multivariate Interpolation with Multiplicities and Simultaneous Polynomial Approximations

Autor: Vincent Neiger, Muhammad F. I. Chowdhury, Gilles Villard, Claude-Pierre Jeannerod, Éric Schost

Publikováno v: IEEE Transactions on Information Theory
IEEE Transactions on Information Theory, 2015, pp.2370-2387. ⟨10.1109/TIT.2015.2416068⟩
IEEE Transactions on Information Theory, Institute of Electrical and Electronics Engineers, 2015, pp.2370-2387. ⟨10.1109/TIT.2015.2416068⟩

The interpolation step in the Guruswami-Sudan algorithm is a bivariate interpolation problem with multiplicities commonly solved in the literature using either structured linear algebra or basis reduction of polynomial lattices. This problem has been

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::cf2e363dc4d7039ad73bc7555514f65a
http://arxiv.org/abs/1402.0643

Fast Computation of Common Left Multiples of Linear Ordinary Differential Operators

Autor: Bruno Salvy, Éric Schost, Romain Lebreton, Muhammad F. I. Chowdhury, Alin Bostan

Publikováno v: ISSAC 2012-37th International Symposium on Symbolic and Algebraic Computation
ISSAC 2012-37th International Symposium on Symbolic and Algebraic Computation, Jul 2012, Grenoble, France. pp.99-106

We study tight bounds and fast algorithms for LCLMs of several linear differential operators with polynomial coefficients. We analyze the arithmetic complexity of existing algorithms for LCLMs, as well as the size of their outputs. We propose a new a

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::893beb6aa5231c9e8fd674d717c29a84

Homotopy techniques for multiplication modulo triangular sets

Autor: Éric Schost, Alin Bostan, Muhammad F. I. Chowdhury, Joris van der Hoeven

Publikováno v: Journal of Symbolic Computation
Journal of Symbolic Computation, Elsevier, 2011, 46 (12), pp.1378-1402. ⟨10.1016/j.jsc.2011.08.015⟩
Journal of Symbolic Computation, 2011, 46 (12), pp.1378-1402. ⟨10.1016/j.jsc.2011.08.015⟩

International audience; We study the cost of multiplication modulo triangular families of polynomials. Following previous work by Li et al. (2007), we propose an algorithm that relies on homotopy and fast evaluation-interpolation techniques. We obtai

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::dd73383419d6f51b4c52766ff6d25107
https://hal.inria.fr/hal-00819155/file/BoChHoSc11.pdf

Effect of Security Increment to Symmetric Data Encryption through AES Methodology

Autor: M. Mia, Muhammad Nazrul Islam, Mohammad Matin, Muhammad F. I. Chowdhury

Publikováno v: SNPD

The selective application of technological and related procedural safeguards is an important responsibility of every organization in providing adequate security to its electronic data systems. Protection of data during transmission or while in storag

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::97d4b8b633250fea7de80b01e1641a39
https://doi.org/10.1109/snpd.2008.101

Complexity and performance results for non FFT-based univariate polynomial multiplication

Autor: Éric Schost, Marc Moreno Maza, Wei Pan, Muhammad F. I. Chowdhury

Publikováno v: ACM Communications in Computer Algebra. 44:99-100

Today's parallel hardware architectures and computer memory hierarchies enforce revisiting fundamental algorithms which were often designed with algebraic complexity as the main complexity measure and with sequential running time as the main performa

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::f0ccebb214a5c2245c66bb27c25fa156
https://doi.org/10.1145/1940475.1940484