Communication-optimal parallel and sequential QR and LU factorizations

Communication-optimal parallel and sequential QR and LU factorizations (2008)

Cached

Download Links

by James Demmel , Laura Grigori , Mark Frederick Hoemmen , Julien Langou

Citations:

BibTeX

@MISC{Demmel08communication-optimalparallel,
    author = {James Demmel and Laura Grigori and Mark Frederick Hoemmen and Julien Langou},
    title = {Communication-optimal parallel and sequential QR and LU factorizations},
    year = {2008}
}

Bookmark

OpenURL

Abstract

Citations

7321	Introduction to Algorithms - Cormen, Leiserson, et al. - 2001
893	Using MPI: Portable Parallel Programming with the Message-Passing Interface - Gropp, Lusk, et al. - 1999
653	Accuracy and Stability of Numerical Algorithms - Higham - 2002
640	The Symmetric Eigenvalue Problem - Parlett - 1998
494	The input/output complexity of sorting and related problems. Commun - AGGARWAL, VITTER - 1988
397	LAPACK’s user’s guide - ANDERSON, BAI, et al. - 1992
306	ScaLAPACK Users' Guide - Blackford - 1997
303	Gaussian elimination is not optimal - STRASSEN - 1969
222	Space-Filling Curves - Sagan - 1994
142	I/O complexity: The red-blue pebble game - HONG, KUNG - 1981
130	for floating-point arithmetic - standard - 2008
84	Locality of reference in LU decomposition with partial pivoting - TOLEDO - 1997
84	A class of parallel tiled linear algebra algorithms for multicore architectures - Buttari, Langou, et al.
83	The block conjugate gradient algorithm and related - O’Leary - 1980
74	Fast Parallel Matrix Inversion Algorithms - Csanky - 1976
63	Recursive blocked algorithms and hybrid data structures for dense matrix library software - Elmroth, Gustavson, et al.
47	A block QMR algorithm for non-Hermitian linear systems with multiple right-hand sides, Linear Algebra and its - Freund, Malhotra - 1997
42	De Geijn. Parallel out-of-core computation and updating of the QR factorization - Gunter, Van
39	An inequality related to the isoperimetric inequality - Loomis, Whitney - 1949
38	On the asymptotic complexity of matrix multiplication - COPPERSMITH, WINOGRAD - 1982
34	Extending the Hong-Kung model to memory hierarchies - SAVAGE - 1995
31	Communication lower bounds for distributed-memory matrix multiplication - IRONY, TOLEDO, et al. - 2004
31	Solving linear least squares problems by Gram-Schmidt orthogonalization - Bjorck - 1967
30	Etude de Quelques Méthodes de Résolution de Problèmes Linéaires de Grande Taille sur Multiprocesseur - Vital - 1990
29	New serial and parallel recursive QR factorization algorithms for SMP systems - ELMROTH, GUSTAVSON - 1998
29	On Stable Parallel Linear System Solvers - Sameh, Kuck - 1978
28	The design and implementation - Choi, Dongarra, et al. - 1996
27	Lapack user’s guide. Society for Industrial and Applied Mathematics - Anderson, Bai, et al. - 1999
26	The design and implementation of the parallel out-of-core ScaLAPACK LU, QR, and Cholesky factorization routines. Concurrency: Practice and Experience - D’Azevedo, Dongarra
24	Predicting structure in nonsymmetric sparse matrix factorizations - Gilbert, Ng - 1993
23	Communication avoiding Gaussian elimination - Grigori, Demmel, et al. - 2008
22	Distributed orthogonal factorization: Givens and householder algorithms - Pothen, Raghavan - 1989
19	A recursive formulation of cholesky factorization of a matrix in packed storage format - Andersen, Gustavson, et al. - 2001
17	Cache-oblivious dynamic programming - CHOWDHURY, RAMACHANDRAN
16	Automatic generation of block-recursive codes - AHMED, PINGALI - 2000
15	Optimal sparse matrix dense vector multiplication in the I/O-model - BENDER, BRODAL, et al. - 2010
13	Some issues in dense linear algebra for multicore and special purpose architectures - Baboulin, Dongarra, et al. - 2008
13	QR factorization for the CELL processor - Kurzak, Dongarra
13	de Geijn, “Scheduling of QR factorization algorithms on SMP and multi-core architectures - Quintana-Ortí, Quintana-Ortí, et al.
12	Fast linear algebra is stable - DEMMEL, DUMITRIU, et al. - 2007
10	Trading Off Parallelism and Numerical Stability - Demmel - 1993
10	Communication-avoiding Krylov subspace methods - Hoemmen - 2010
9	High performance Cholesky factorization via blocking and recursion that uses minimal storage - Gustavson, Jonsson - 2001
9	standard for floating-point arithmetic - IEEE - 2008
8	An alternative Givens ordering - Modi, Clarke - 1984
7	off error analysis for Gram–Schmidt method and solution of linear least squares problems - Abdelmalek, Round - 1971
6	Strakoˇs: Numerical behavior of the modified GramSchmidt GMRES implementation - Greenbaum, Rozloˇzník, et al. - 1997
6	Basis selection in LOBPCG - Hetmaniuk, Lehoucq
6	Design of scalable dense linear algebra libraries for multithreaded architectures: The LU factorization - Quintana-Ortí, Quintana-Ortí, et al. - 2008
6	A block orthogonalization procedure with constant synchronization requirements - Stathopoulos, Wu - 2002