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ISSAC
2007
Springer
105views Mathematics» more  ISSAC 2007»
14 years 1 months ago
Certification of the QR factor R and of lattice basis reducedness
Given a lattice basis of n vectors in Zn, we propose an algorithm using 12n3 + O(n2) floating point operations for checking whether the basis is LLL-reduced. If the basis is redu...
Gilles Villard
CORR
2008
Springer
76views Education» more  CORR 2008»
13 years 7 months ago
Communication-avoiding parallel and sequential QR factorizations
We present parallel and sequential dense QR factorization algorithms that are optimized to avoid communication. Some of these are novel, and some extend earlier work. Communicatio...
James Demmel, Laura Grigori, Mark Hoemmen, Julien ...
EUROPAR
2011
Springer
12 years 7 months ago
A Fully Empirical Autotuned Dense QR Factorization for Multicore Architectures
: Tuning numerical libraries has become more difficult over time, as systems get more sophisticated. In particular, modern multicore machines make the behaviour of algorithms hard ...
Emmanuel Agullo, Jack Dongarra, Rajib Nath, Stanim...
TPDS
2010
174views more  TPDS 2010»
13 years 6 months ago
Parallel Two-Sided Matrix Reduction to Band Bidiagonal Form on Multicore Architectures
The objective of this paper is to extend, in the context of multicore architectures, the concepts of tile algorithms [Buttari et al., 2007] for Cholesky, LU, QR factorizations to t...
Hatem Ltaief, Jakub Kurzak, Jack Dongarra
DIS
2004
Springer
14 years 1 months ago
Tiling Databases
Abstract. In this paper, we consider 0/1 databases and provide an alternative way of extracting knowledge from such databases using tiles. A tile is a region in the database consis...
Floris Geerts, Bart Goethals, Taneli Mielikäi...