Tiled QR factorization algorithms

Abstract : This work revisits existing algorithms for the QR factorization of rectangular matrices composed of p x q tiles, where p is greater or equal than q. Within this framework, we study the critical paths and performance of algorithms such as Sameh-Kuck, Fibonacci, Greedy, and those found within PLASMA. Although neither Fibonacci nor Greedy is optimal, both are shown to be asymptotically optimal for all matrices of size p = q2 f(q), where f is any function such that limit of f is 0. This result applies to all matrices where p and q are proportional, p = lambda x q, with lambda greater than 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 and skinny matrices.
Complete list of metadatas

Cited literature [17 references]  Display  Hide  Download

https://hal.inria.fr/inria-00585721
Contributor : Mathias Jacquelin <>
Submitted on : Friday, April 22, 2011 - 3:21:29 PM
Last modification on : Saturday, July 27, 2019 - 1:15:12 AM
Long-term archiving on : Thursday, March 30, 2017 - 9:45:11 AM

File

RR-7601.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : inria-00585721, version 3

Collections

Citation

Henricus Bouwmeester, Mathias Jacquelin, Julien Langou, Yves Robert. Tiled QR factorization algorithms. [Research Report] RR-7601, INRIA. 2011, pp.32. ⟨inria-00585721v3⟩

Share

Metrics

Record views

257

Files downloads

388