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arXiv.org e-Print Archive
Preprint . 2008
Data sources: arXiv.org e-Print Archive
https://dx.doi.org/10.48550/ar...
Article . 2008
License: arXiv Non-Exclusive Distribution
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Communication-optimal parallel and sequential QR and LU factorizations: theory and practice

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2008Embargo end date: 01 Jan 2008Publisher:arXiv
Authors: Demmel, James; Grigori, Laura; Hoemmen, Mark; Langou, Julien;

doi: 10.48550/arxiv.0806.2159

arXiv: 0806.2159

Communication-optimal parallel and sequential QR and LU factorizations: theory and practice

Abstract

We present parallel and sequential dense QR factorization algorithms that are both optimal (up to polylogarithmic factors) in the amount of communication they perform, and just as stable as Householder QR. Our first algorithm, Tall Skinny QR (TSQR), factors m-by-n matrices in a one-dimensional (1-D) block cyclic row layout, and is optimized for m >> n. Our second algorithm, CAQR (Communication-Avoiding QR), factors general rectangular matrices distributed in a two-dimensional block cyclic layout. It invokes TSQR for each block column factorization.

Keywords

FOS: Mathematics, Mathematics - Numerical Analysis, Numerical Analysis (math.NA)

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
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