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dc.contributor.authorChiu, Jiawei
dc.contributor.authorDemanet, Laurent
dc.date.accessioned2012-07-26T17:49:36Z
dc.date.available2012-07-26T17:49:36Z
dc.date.issued2012-02
dc.date.submitted2011-11
dc.identifier.issn0036-1429
dc.identifier.urihttp://hdl.handle.net/1721.1/71842
dc.description.abstractWhen a matrix A with n columns is known to be well-approximated by a linear combination of basis matrices B1, . . . , Bp, we can apply A to a random vector and solve a linear system to recover this linear combination. The same technique can be used to obtain an approximation to A[superscript −1]. A basic question is whether this linear system is well-conditioned. This is important for two reasons: a well-conditioned system means (1) we can invert it and (2) the error in the reconstruction can be controlled. In this paper, we show that if the Gram matrix of the Bj ’s is sufficiently well-conditioned and each Bj has a high numerical rank, then n [infinity symbol] p log[superscript 2] n will ensure that the linear system is well-conditioned with high probability. Our main application is probing linear operators with smooth pseudodifferential symbols such as the wave equation Hessian in seismic imaging [L. Demanet et al., Appl. Comput. Harmonic Anal., 32 (2012), pp. 155–168]. We also demonstrate numerically that matrix probing can produce good preconditioners for inverting elliptic operators in variable media.en_US
dc.description.sponsorshipAlfred P. Sloan Foundationen_US
dc.description.sponsorshipNational Science Foundation (U.S.)en_US
dc.description.sponsorshipSingapore-MIT Alliance for Research and Technologyen_US
dc.language.isoen_US
dc.publisherSociety for Industrial and Applied Mathematicsen_US
dc.relation.isversionofhttp://dx.doi.org/10.1137/110825972en_US
dc.rightsArticle is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.en_US
dc.sourceSIAMen_US
dc.titleMatrix Probing and its Conditioningen_US
dc.typeArticleen_US
dc.identifier.citationChiu, Jiawei, and Laurent Demanet. “Matrix Probing and Its Conditioning.” SIAM Journal on Numerical Analysis 50.1 (2012): 171–193. Web.en_US
dc.contributor.departmentMassachusetts Institute of Technology. Department of Mathematicsen_US
dc.contributor.approverDemanet, Laurent
dc.contributor.mitauthorChiu, Jiawei
dc.contributor.mitauthorDemanet, Laurent
dc.relation.journalSIAM Journal on Numerical Analysisen_US
dc.eprint.versionFinal published versionen_US
dc.type.urihttp://purl.org/eprint/type/JournalArticleen_US
eprint.statushttp://purl.org/eprint/status/PeerRevieweden_US
dspace.orderedauthorsChiu, Jiawei; Demanet, Laurenten
dc.identifier.orcidhttps://orcid.org/0000-0001-7052-5097
mit.licensePUBLISHER_POLICYen_US


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