dc.contributor.author | Christianson, Bruce | |
dc.date.accessioned | 2018-08-16T00:14:48Z | |
dc.date.available | 2018-08-16T00:14:48Z | |
dc.date.issued | 2018-11-02 | |
dc.identifier.citation | Christianson , B 2018 , ' Differentiating through Conjugate Gradient ' , Optimization Methods and Software , vol. 33 , no. 4-6 , pp. 988-994 . https://doi.org/10.1080/10556788.2018.1425862 | |
dc.identifier.issn | 1055-6788 | |
dc.identifier.uri | http://hdl.handle.net/2299/20409 | |
dc.description | This is the pre-print version of an article published by Taylor & Francis in Optimization Methods and Software on 6 January 2018, available online at: https://doi.org/10.1080/10556788.2018.1425862. | |
dc.description.abstract | We show that, although the Conjugate Gradient (CG) Algorithm has a singularity at the solution, it is possible to differentiate forward through the algorithm automatically by re-declaring all the variables as truncated Taylor series, the type of active variable widely used in Automatic Differentiation (AD) tools such as ADOL-C. If exact arithmetic is used, this approach gives a complete sequence of correct directional derivatives of the solution, to arbitrary order, in a single cycle of at most n iterations, where n is the number of dimensions. In the inexact case the approach emphasizes the need for a means by which the programmer can communicate certain conditions involving derivative values directly to an AD tool. | en |
dc.format.extent | 7 | |
dc.format.extent | 285429 | |
dc.format.extent | 312391 | |
dc.language.iso | eng | |
dc.relation.ispartof | Optimization Methods and Software | |
dc.subject | Automatic differentiation | |
dc.subject | Taylor series | |
dc.subject | conjugate gradient | |
dc.subject | Software | |
dc.subject | Control and Optimization | |
dc.subject | Applied Mathematics | |
dc.title | Differentiating through Conjugate Gradient | en |
dc.contributor.institution | Centre for Computer Science and Informatics Research | |
dc.description.status | Peer reviewed | |
dc.date.embargoedUntil | 2019-01-26 | |
dc.identifier.url | http://www.scopus.com/inward/record.url?scp=85053272150&partnerID=8YFLogxK | |
rioxxterms.versionofrecord | 10.1080/10556788.2018.1425862 | |
rioxxterms.type | Journal Article/Review | |
herts.preservation.rarelyaccessed | true | |