Show simple item record

dc.contributor.authorChristianson, B.
dc.date.accessioned2010-03-16T09:50:10Z
dc.date.available2010-03-16T09:50:10Z
dc.date.issued1992
dc.identifier.citationChristianson , B 1992 , ' Reverse accumulation and accurate rounding error estimates for taylor series coefficient ' , Optimization Methods and Software , vol. 1 , no. 1 , pp. 81-94 . https://doi.org/10.1080/10556789208805508
dc.identifier.issn1055-6788
dc.identifier.otherPURE: 102663
dc.identifier.otherPURE UUID: 48be4070-1004-48bd-bb9b-310035f654c9
dc.identifier.otherdspace: 2299/4336
dc.identifier.otherScopus: 0026862533
dc.identifier.urihttp://hdl.handle.net/2299/4336
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 extending the technique of reverse accumulation so as to obtain gradients of univariate Taylor series coefficients. This is done by re-interpreting the same formulae used to reverse accumulategradients in the conventional (scalar) case. Thus a carefully written implementation of conventional reverse accumulation can be extended to the Taylor series valued case by (further) overloading of the appropriate operators. Next, we show how to use this extended reverse accumulation technique so as to construct accurate (i.e. rigorous and sharp) error bounds for the numerical values of the Taylor series coefficients of the target function, again by re-interpreting the corresponding conventional (scalar) formulae. This extension can also be implemented simply by re-engineering existing code. The two techniques (reverse accumulation of gradients and accurate error estimates) each require only a small multiple of the processing time required to compute the underlying Taylor series coefficients. Space "requirements are comparable to those for conventional (scalar) reverse accumulation, and can be simply managed. We concluded with a discussion of possible implementation strategies and the implications for the re-use of code.en
dc.language.isoeng
dc.relation.ispartofOptimization Methods and Software
dc.titleReverse accumulation and accurate rounding error estimates for taylor series coefficienten
dc.contributor.institutionSchool of Computer Science
dc.contributor.institutionCentre for Computer Science and Informatics Research
dc.description.statusPeer reviewed
rioxxterms.versionofrecordhttps://doi.org/10.1080/10556789208805508
rioxxterms.typeJournal Article/Review
herts.preservation.rarelyaccessedtrue


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record