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Accession Number ADA584728
Title Communication Avoiding Rank Revealing QR Factorization with Column Pivoting.
Publication Date May 2013
Media Count 44p
Personal Author H. Xiang J. W. Demmel L. Grigori M. Gu
Abstract In this paper we introduce CARRQR, a communication avoiding rank revealing QR factorization with tournament pivoting. We show that CARRQR reveals the numerical rank of a matrix in an analogous way to QR factorization with column pivoting (QRCP). Although the upper bound of a quantity involved in the characterization of a rank revealing factorization is worse for CARRQR than for QRCP, our numerical experiments on a set of challenging matrices show that this upper bound is very pessimistic, and CARRQR is an effective tool in revealing the rank in practical problems. Our main motivation for introducing CARRQR is that it minimizes data transfer, modulo poly- logarithmic factors, on both sequential and parallel machines, while previous factorizations as QRCP are communication sub-optimal and require asymptotically more communication than CARRQR. Hence CARRQR is expected to have a better performance on current and future computers, where communication is a major bottleneck that highly impacts the performance of an algorithm.
Keywords Algorithms
Column pivoting
Communication avoiding
Communication optimal algorithms
Computation science
Computations
Data transfer
Matrices(Mathematics)
Minimize communication
Parallel processing
Qr factorization
Rank revealing
Ranking
Tournament pivoting

 
Source Agency Non Paid ADAS
NTIS Subject Category 72B - Algebra, Analysis, Geometry, & Mathematical Logic
Corporate Author California Univ., Berkeley. Dept. of Electrical Engineering and Computer Science.
Document Type Technical report
Title Note Technical rept.
NTIS Issue Number 1403
Contract Number HR0011-12-2-0016

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