Show simple item record

dc.contributor.authorBeltrán Álvarez, Carlos 
dc.contributor.authorDedieu, Jean-Pierre
dc.contributor.authorMalajovich, Gregorio
dc.contributor.authorShub, Michael
dc.contributor.otherUniversidad de Cantabriaes_ES
dc.date.accessioned2013-09-12T06:46:31Z
dc.date.available2013-09-12T06:46:31Z
dc.date.issued2012-08
dc.identifier.issn0895-4798
dc.identifier.issn1095-7162
dc.identifier.urihttp://hdl.handle.net/10902/3206
dc.description.abstractIn our previous paper [SIAM J. Matrix Anal. Appl., 31 (2010), pp. 1491–1506], we studied the condition metric in the space of maximal rank n × m matrices. Here, we show that this condition metric induces a Lipschitz Riemannian structure on that space. After investigating geodesics in such a nonsmooth structure, we show that the inverse of the smallest singular value of a matrix is a log-convex function along geodesics. We also show that a similar result holds for the solution variety of linear systems. Some of our intermediate results such as those on the second covariant derivative or Hessian of a function with symmetries on a manifold, and those on piecewise self-convex functions, are of independent interest. Those results were motivated by our investigations on the complexity of path-following algorithms for solving polynomial systems.es_ES
dc.format.extent35 p.es_ES
dc.language.isoenges_ES
dc.publisherSociety for Industrial and Applied Mathematicses_ES
dc.rights© 2012 Society for Industrial and Applied Mathematicses_ES
dc.sourceSIAM Journal on Matrix Analysis and Applications, Vol. 33, No. 3, pp. 905–939es_ES
dc.subject.otherCondition numberes_ES
dc.subject.otherLipschitz Riemannian structurees_ES
dc.subject.otherConvexityes_ES
dc.subject.otherSelf-convexityes_ES
dc.titleConvexity properties of the condition number IIes_ES
dc.typeinfo:eu-repo/semantics/articlees_ES
dc.relation.publisherVersionhttp://dx.doi.org/10.1137/100808885es_ES
dc.rights.accessRightsopenAccesses_ES
dc.identifier.DOI10.1137/100808885
dc.type.versionpublishedVersiones_ES


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record