Convergence properties of the Barzilai and Borwein gradient method

Simple item page
dc.contributor.advisorTapia, Richard A.en_US
dc.contributor.advisorDennis, John E., Jr.en_US
dc.creatorRaydan M., Marcosen_US
dc.date.accessioned2009-06-04T00:37:06Zen_US
dc.date.available2009-06-04T00:37:06Zen_US
dc.date.issued1991en_US
dc.description.abstractIn a recent paper, Barzilai and Borwein presented a new choice of steplength for the gradient method. Their choice does not guarantee descent in the objective function and greatly speeds up the convergence of the method. We derive an interesting relationship between any gradient method and the shifted power method. This relationship allows us to establish the convergence of the Barzilai and Borwein method when applied to the problem of minimizing any strictly convex quadratic function (Barzilai and Borwein considered only 2-dimensional problems). Our point of view also allows us to explain the remarkable improvement obtained by using this new choice of steplength. For the two eigenvalues case we present some very interesting convergence rate results. We show that our Q and R-rate of convergence analysis is sharp and we compare it with the Barzilai and Borwein analysis. We derive the preconditioned Barzilai and Borwein method and present preliminary numerical results indicating that it is an effective method, as compared to the preconditioned Conjugate Gradient method, for the numerical solution of some special symmetric positive definite linear systems that arise in the numerical solution of Partial Differential Equations.en_US
dc.format.extent60 p.en_US
dc.format.mimetypeapplication/pdfen_US
dc.identifier.callnoThesis Math. Sci. 1991 Raydanen_US
dc.identifier.citationRaydan M., Marcos. "Convergence properties of the Barzilai and Borwein gradient method." (1991) Diss., Rice University. <a href="https://hdl.handle.net/1911/16479">https://hdl.handle.net/1911/16479</a>.en_US
dc.identifier.urihttps://hdl.handle.net/1911/16479en_US
dc.language.isoengen_US
dc.rightsCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.en_US
dc.subjectMathematicsen_US
dc.subjectOperations researchen_US
dc.titleConvergence properties of the Barzilai and Borwein gradient methoden_US
dc.typeThesisen_US
dc.type.materialTexten_US
thesis.degree.departmentMathematical Sciencesen_US
thesis.degree.disciplineEngineeringen_US
thesis.degree.grantorRice Universityen_US
thesis.degree.levelDoctoralen_US
thesis.degree.nameDoctor of Philosophyen_US
Files
Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
9136065.PDF
Size:
1.53 MB
Format:
Adobe Portable Document Format
Download
Collections
Rice University Theses and Dissertations