LU factorization algorithms on distributed-memory multiprocessor architectures

Technical Report · Sun Mar 01 04:00:00 EST 1987

OSTI ID:6684241

Geist, G A; Romine, C H

In this paper, we consider the effect that the data storage scheme and pivoting scheme have on the efficiency of LU factorization on a distributed-memory multiprocessor. Our presentation will focus on the hypercube architecture, but most of our results are applicable to distributed-memory architectures generally. We restrict our attention to two commonly used storage schemes (storage by rows and by columns) and investigate partial pivoting both by rows and by columns, yielding four factorization algorithms. The goal is to determine which of these four algorithms admits the most efficient parallel implementation. We analyze factors such as load distribution, pivoting cost, and potential for pipelining. We conclude that, in the absence of loop unrolling, LU factorization with partial pivoting is most efficient when pipelining is used to mask the cost of pivoting. The two schemes that can be pipelined are pivoting by interchanging rows when the coefficient matrix is distributed to the processors by columns, and pivoting by interchanging columns when the matrix is distributed to the processors by rows.

• Research Organization: Oak Ridge National Lab., TN (USA)
• DOE Contract Number: AC05-84OR21400
• OSTI ID: 6684241
• Report Number(s): ORNL/TM-10383; ON: DE87007794
• Country of Publication: United States
• Language: English

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