Abstract
In the search for regions that contain fixed points ofa real
function of several variables, tests based on interval
calculationscan be used to establish existence ornon-existence of
fixed points in regions that are examined in the course ofthe
search. The search can e.g. be performed as a synchronous
(sequential) interval iteration:In each iteration step all
components of the iterate are calculatedbased on the previous
iterate. In this case it is straight forward to base simple
interval existence and non-existencetests on the calculations done
in each step of the iteration. The search can also be performed as
an asynchronous (parallel) iteration: Only a few components are
changed in each stepand this calculation is in general based on
components from differentprevious iterates. For the asynchronous
iteration it turns out thatsimple tests of existence and
non-existence can be based on thecomponentwise calculations done
in the course of the iteration. These componentwisetests are
useful for parallel implementation of the search, sincethe tests
can then be performed local to each processor and only when a test
issuccessful do a processor communicate this result to other
processors.
Original language | English |
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Journal | Reliable Computing |
Volume | 3 |
Pages (from-to) | 259-268 |
ISSN | 1385-3139 |
Publication status | Published - 1997 |