A Parallel QR Factorization Algorithm with Controlled Local Pivoting

This paper presents a new version of the Householder algorithm with column pivoting for computing a QR factorization that identifies rank and range space of a given matrix. The standard pivoting technique is not well suited for parallel computation, since it requires synchronization at every step in...

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Bibliographic Details
Published in:SIAM journal on scientific and statistical computing Vol. 12; no. 1; pp. 36 - 57
Main Author: Bischof, Christian H.
Format: Journal Article
Language:English
Published: Philadelphia, PA Society for Industrial and Applied Mathematics 01.01.1991
Subjects:
Algorithms
Exact sciences and technology
Laboratories
Linear algebra
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Numerical linear algebra
Sciences and techniques of general use
Parallel algorithm
Mathematical matrix
Pivoting method
Distributed system
MIMD computer
ISSN:0196-5204, 1064-8275, 2168-3417, 1095-7197
Online Access:Get full text
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Summary:This paper presents a new version of the Householder algorithm with column pivoting for computing a QR factorization that identifies rank and range space of a given matrix. The standard pivoting technique is not well suited for parallel computation, since it requires synchronization at every step in order to choose the next pivot column. In contrast, a restricted pivoting scheme that restricts the choice of pivot columns and avoids this synchronization constraint is employed. Incremental condition estimation is used to assess the effect that the addition of a candidate pivot column would have on the condition number of the matrix being generated. This safeguard ensures that this local strategy selects pivot columns that make sense in the global context of the computation. The resulting algorithm is well suited for implementation on a parallel machine, in particular, a MIMD machine with distributed memory. Simulations demonstrate that the numerical behavior of the restricted pivoting strategy is comparable to the traditional global pivoting strategy. Implementation results of the QR factorization algorithm without pivoting and with local and traditional pivoting on the Intel iPSC/1 and iPSC/2 hypercubes show that our scheme about halves the extra time required for pivoting.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
content type line 14
ISSN:0196-5204
1064-8275
2168-3417
1095-7197
DOI:10.1137/0912002