(no subject)

Dear Colleagues,

Here are some questions posed by Iain Duff ([email protected])  to stimulate 
some discussion in the CSC list serve. Please prove that you are back from 
your vacations and getting back to fun and CSC by your contribution :-) 
--Alex 


Several direct codes, notably SuperLU, PARDISO, and MA57 in different ways 
restrict the pivoting during numerical factorization so that the 
structures determined during the analysis can be respected.  This clearly 
has important implications for limiting storage and for parallelism.
Normally if it is necessary to use a pivot that does not satisfy the 
numerical criterion it is replaced by some suitable value (conventionally
||A||*sqrt(epsilon)) and the factorization proceeds.  This will of course 
result in the factorization of a perturbed matrix but hopefully 
perturbations are small and so the solution is obtained by a simple 
iterative method.

My question to the group is what term should we use to describe this kind 
of strategy.  We [1] have used the term "static pivoting" and believe that 
this was first used in [2]. Is this indeed the first reference to this 
term and when was the term first used in a journal paper?  Is it an 
appropriate term to use or is there a more appropriate term?  The debate 
is open.

[1]
@techreport{dupr:05a,
    author = {Iain S. Duff and St\'ephane Pralet},
    title = {Towards a stable static pivoting strategy for the sequential 
and
             parallel solution of sparse symmetric indefinite systems},
    institution = RAL,
    number = {RAL-TR-2005-007},
    notes  = {Also appeared as report TR/PA/05/26, CERFACS, Toulouse
              and report RT/TLSE/05/08, IRIT, ENSEEIHT, Toulouse},
    year = {2005} }

[2]
@inproceedings{lide:98,
    AUTHOR = {Xiaoye S. Li and James W. Demmel},
    TITLE = {Making Sparse {G}aussian Elimination Scalable by Static
                  Pivoting},
    BOOKTITLE = {Proceedings of Supercomputing},
    ADDRESS = {Orlando, Florida},
    YEAR = {1998},
    MONTH = {November}
}
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