On Consistency Properties of Discrete Adjoint Linear Multistep Methods

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dc.contributor.authorSandu, Adrianen
dc.contributor.departmentComputer Scienceen
dc.date.accessioned2013-06-19T14:36:15Zen
dc.date.available2013-06-19T14:36:15Zen
dc.date.issued2007en
dc.description.abstractIn this paper we analyze the consistency properties of discrete adjoints of linear multistep methods. Discrete adjoints are very popular in optimization and control since they can be constructed automatically by reverse mode automatic differentiation. The consistency analysis reveals that the discrete linear multistep adjoints are, in general, inconsistent approximations of the adjoint ODE solution along the trajectory. However, the discrete adjoints at the initial time (and therefore the discrete adjoint gradients) converge to the adjoint ODE solution with the same order as the original linear multistep method. Discrete adjoints inherit the zero-stability properties of the forward method. Numerical results confirm the theoretical findings.en
dc.format.mimetypeapplication/pdfen
dc.identifierhttp://eprints.cs.vt.edu/archive/00001007/en
dc.identifier.sourceurlhttp://eprints.cs.vt.edu/archive/00001007/01/dadj_lmm_report.pdfen
dc.identifier.trnumberTR-07-40en
dc.identifier.urihttp://hdl.handle.net/10919/19773en
dc.language.isoenen
dc.publisherDepartment of Computer Science, Virginia Polytechnic Institute & State Universityen
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subjectNumerical analysisen
dc.titleOn Consistency Properties of Discrete Adjoint Linear Multistep Methodsen
dc.typeTechnical reporten
dc.type.dcmitypeTexten

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