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...
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 ...
: 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...
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...
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...