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... preconditioner.% latex2html id marker 3333 \setcounter{footnote}{5}\fnsymbol{footnote}
In fact, they are the starting points of both classes of sweeping preconditioners. The $ \mathcal{H}$ -matrix approach essentially executes these algorithms with $ \mathcal{H}$ -matrix arithmetic. 
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....% latex2html id marker 3377 \setcounter{footnote}{6}\fnsymbol{footnote}
In all of the experiments in this paper, $ \gamma(\omega)$ was either 5 or 6, and the subdomain depth never exceeded 10. 
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....% latex2html id marker 3465 \setcounter{footnote}{7}\fnsymbol{footnote}
Note that increasing the number of planes per panel provides a mechanism for interpolating between the sweeping preconditioner and a full multifrontal factorization. 
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... sequentially.% latex2html id marker 3518 \setcounter{footnote}{8}\fnsymbol{footnote}
While it is tempting to try to expose more parallelism with techniques like cyclic reduction (which is a special case of a multifrontal algorithm), their straightforward application destroys the Schur complement properties that we exploit for our fast algorithm. 
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...Schreiber-scalability.% latex2html id marker 3529 \setcounter{footnote}{9}\fnsymbol{footnote}
Cf. (1), which advocates for only distributing the root frontal matrix two-dimensionally and using a one-dimensional distribution for all other fronts. 
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... processes.
In cases where the available solve parallelism has been exhausted but the problem cannot be solved on less processes due to memory constraints, it would be preferable to solve with subdomains stored on subsets of processes. 
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... frequency.
A similar observation is also made in (37). 
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... implemented.
Other than Clique, the only other implementation appears to be in DSCPACK (31). 
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