A panorama of positivity. II: Fixed dimension
dc.contributor.author | Belton, Alexander | |
dc.contributor.author | Guillot, D | |
dc.contributor.author | Khare, A | |
dc.contributor.author | Putinar, M | |
dc.date.accessioned | 2023-02-13T10:21:06Z | |
dc.date.available | 2023-02-13T10:21:06Z | |
dc.date.issued | 2020 | |
dc.identifier.issn | 0271-4132 | |
dc.identifier.issn | 1098-3627 | |
dc.identifier.uri | http://hdl.handle.net/10026.1/20268 | |
dc.description.abstract |
This survey contains a selection of topics unified by the concept of positive semidefiniteness (of matrices or kernels), reflecting natural constraints imposed on discrete data (graphs or networks) or continuous objects (probability or mass distributions). We put emphasis on entrywise operations which preserve positivity, in a variety of guises. Techniques from harmonic analysis, function theory, operator theory, statistics, combinatorics, and group representations are invoked. Some partially forgotten classical roots in metric geometry and distance transforms are presented with comments and full bibliographical references. Modern applications to high-dimensional covariance estimation and regularization are included. | |
dc.format.extent | 109-150 | |
dc.language.iso | en | |
dc.publisher | American Mathematical Society | |
dc.rights | Attribution-NonCommercial-NoDerivatives 4.0 International | |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | |
dc.subject | metric geometry | |
dc.subject | positive semidefinite matrix | |
dc.subject | Toeplitz matrix | |
dc.subject | Hankel matrix | |
dc.subject | positive definite function | |
dc.subject | completely monotone functions | |
dc.subject | absolutely monotonic functions | |
dc.subject | entrywise calculus | |
dc.subject | generalized Vandermonde matrix | |
dc.subject | Schur polynomials | |
dc.subject | symmetric function | |
dc.subject | identities | |
dc.subject | totally positive matrices | |
dc.subject | totally non-negative matrices | |
dc.subject | totally positive completion problem | |
dc.subject | sample covariance | |
dc.subject | covariance estimation | |
dc.subject | hard / soft thresholding | |
dc.subject | sparsity pattern | |
dc.subject | critical exponent of a graph | |
dc.subject | chordal graph | |
dc.subject | Loewner monotonicity | |
dc.subject | convexity | |
dc.subject | and super-additivity | |
dc.title | A panorama of positivity. II: Fixed dimension | |
dc.type | conference | |
dc.type | Chapter | |
plymouth.author-url | https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000564770600005&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=11bb513d99f797142bcfeffcc58ea008 | |
plymouth.volume | 743 | |
plymouth.publication-status | Published | |
plymouth.journal | Complex Analysis and Spectral Theory | |
dc.identifier.doi | 10.1090/conm/743/14958 | |
plymouth.organisational-group | /Plymouth | |
plymouth.organisational-group | /Plymouth/Faculty of Science and Engineering | |
plymouth.organisational-group | /Plymouth/Faculty of Science and Engineering/School of Engineering, Computing and Mathematics | |
plymouth.organisational-group | /Plymouth/Users by role | |
plymouth.organisational-group | /Plymouth/Users by role/Academics | |
dcterms.dateAccepted | 2019-05-19 | |
dc.rights.embargodate | 2023-2-25 | |
dc.identifier.eissn | 1098-3627 | |
dc.rights.embargoperiod | Not known | |
rioxxterms.versionofrecord | 10.1090/conm/743/14958 | |
rioxxterms.licenseref.uri | http://creativecommons.org/licenses/by-nc-nd/4.0/ | |
rioxxterms.type | Journal Article/Review |