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Partitioning Using PAQ

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Abstract

The so-called PAQ problem is concerned with the solution of sparse systems of linear equations Ax=b using the transformation PAQy=Pb,x=Qy. An algorithm is given for choosing P and Q to partition the matrix A into its irreducible components. A theorem on which this algorithm is based has long been known, yet no simple, easily understood proof appears in the literature. Such a proof is given here. Remarks are made concerning some unsolved problems related to the PAQ problem.

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1975-08

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Cornell University

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computer science; technical report

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http://techreports.library.cornell.edu:8081/Dienst/UI/1.0/Display/cul.cs/TR75-256

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technical report

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