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dc.contributor.authorChristianson, B.
dc.date.accessioned2010-03-16T12:12:12Z
dc.date.available2010-03-16T12:12:12Z
dc.date.issued1998
dc.identifier.citationChristianson , B 1998 , ' Reverse accumulation and implicit functions ' , Optimization Methods and Software , vol. 9 , no. 4 , pp. 307-322 . https://doi.org/10.1080/10556789808805697
dc.identifier.issn1055-6788
dc.identifier.otherPURE: 97407
dc.identifier.otherPURE UUID: 4f6e9b88-ace4-4199-846e-34342ec70264
dc.identifier.otherdspace: 2299/4341
dc.identifier.otherScopus: 0031639751
dc.identifier.urihttp://hdl.handle.net/2299/4341
dc.descriptionOriginal article can be found at: http://www.informaworld.com/smpp/title~content=t713645924~db=all Copyright Taylor and Francis / Informa.
dc.description.abstractWe begin by introducing a simple technique for using reverse accumulation the first derivatives of target functions which include in their construction the solution of systems of linear or nonlinear equations. In the linear case solving Ay= b for y corresponds to the adjoint operations [...] where vis the solution to the adjoint equations vA=y. A more sophisticated construction applies in the nonlinear case. We apply these technique to obtain automatic numerical error estimates for calculated function values. These error estimates include the effects of inaccurate equation solution as well as rounding error. Our basic techniques can be generalized to functions which contain several (linear or nonlinear) implicit functions in their construction, either serially or nested. In the case of scalar-valued target functions that include equation solution as part of their construction. Our algorithms involve at most the same order of computational effort as the computation of the target function value, regardless of the number of independent variables or the size of the systems of equations.en
dc.language.isoeng
dc.relation.ispartofOptimization Methods and Software
dc.rights/dk/atira/pure/core/openaccesspermission/open
dc.titleReverse accumulation and implicit functionsen
dc.contributor.institutionSchool of Computer Science
dc.description.statusPeer reviewed
dc.relation.schoolSchool of Computer Science
rioxxterms.versionofrecordhttps://doi.org/10.1080/10556789808805697
rioxxterms.typeJournal Article/Review
herts.preservation.rarelyaccessedtrue
herts.rights.accesstyperestrictedAccess


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