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dc.contributor.authorChristianson, B.
dc.date.accessioned2010-03-16T11:17:45Z
dc.date.available2010-03-16T11:17:45Z
dc.date.issued1994
dc.identifier.citationChristianson , B 1994 , ' Reverse accumulation and attractive fixed points ' , Optimization Methods and Software , vol. 3 , no. 4 , pp. 311-326 . https://doi.org/10.1080/10556789408805572
dc.identifier.issn1055-6788
dc.identifier.otherPURE: 102707
dc.identifier.otherPURE UUID: 12eb86b2-7760-4e20-b9be-8d62f5fc145a
dc.identifier.otherdspace: 2299/4338
dc.identifier.otherScopus: 0028698107
dc.identifier.urihttp://hdl.handle.net/2299/4338
dc.descriptionOriginal article can be found at: http://www.informaworld.com/smpp/title~content=t713645924~db=all Copyright Taylor and Francis / Informa. [Originally issued in 1992 as UH Technical Report 258]
dc.description.abstractWe apply reverse accumulation to obtain automatic gradients and error estimates of functions which include in their computation a convergent iteration of the form y= Φ(y,u), where y and u are vectors. We suggest an implementation approach which allows this to be done by a fairly routine extension of existing reverse accumulation code. We show how to re-use the computational graph for the fixed point constructor Φ so as to set explicit stopping criteria for the iterations, based on the gradient accuracy required. Our construction allows the gradient vector to be obtained to the same order of accuracy as the objective function values (which is in general the best we can hope to achieve), and the same order of computational cost (which does not explicitly depend upon the number of independent variables.) The technique can be applied to functions which contain several iterative constructions, either serially or nested.en
dc.language.isoeng
dc.relation.ispartofOptimization Methods and Software
dc.rightsOpen
dc.titleReverse accumulation and attractive fixed pointsen
dc.contributor.institutionSchool of Computer Science
dc.contributor.institutionCentre for Computer Science and Informatics Research
dc.description.statusPeer reviewed
dcterms.dateAccepted1994
rioxxterms.versionofrecordhttps://doi.org/10.1080/10556789408805572
rioxxterms.typeJournal Article/Review
herts.preservation.rarelyaccessedtrue
herts.rights.accesstypeOpen


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