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SCHEDULE: NOV 12-18, 2011

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Tiled QR factorization algorithms

SESSION: Dense Linear Algebra


TIME: 11:00AM - 11:30AM

AUTHOR(S):Henricus M. Bouwmeester, Mathias Jacquelin, Julien Langou, Yves Robert


This work revisits existing algorithms for the QR factorization of rectangular matrices composed of $p times q$ tiles, where $p geq q$. Within this framework, we study the critical paths and performance of algorithms such as SK, MC, Greedy, and those found within PLASMA. Although neither MC nor Greedy is optimal, both are shown to be asymptotically optimal for all matrices of size $p = q^2 f(q)$, where $f$ is any function such that $lim_{+infty} f= 0$. This result applies to all matrices where $p$ and $q$ are proportional, $ p = lambda q$, with $lambda geq 1$, thereby encompassing many important situations in practice (least squares). We provide an extensive set of experiments that show the superiority of the new algorithms for tall matrices.

Chair/Author Details:

Henricus M. Bouwmeester - University of Colorado Denver

Mathias Jacquelin - ENS Lyon

Julien Langou - University of Colorado Denver

Yves Robert - ENS Lyon

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The full paper can be found in the ACM Digital Library

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