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H.W. van Dijk and E.F. Deprettere
The operators are otherwise said to be dependent. If independent, then the application of
the implication
MilJ Mplq =~ MPlq MilJ
is called a
dependence preserving transformation
step.
For any particular Jacobi-type algorithm, the behaviour of the operators in a slice are well
defined and it is, then, easy to express where independent operations, if any, can be found.
The independency property makes explicit that the ordering of the operators in a slice for a
certain DG is not unique. In fact we exploit this property to detect the critical path in the
algorithm. The critical path ...