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Article: Birkhoff-von Neumann theorem for multistochastic tensors
| Title | Birkhoff-von Neumann theorem for multistochastic tensors |
|---|---|
| Authors | |
| Keywords | Multistochastic tensors Permutation tensors Permanent Doubly stochastic matrices |
| Issue Date | 2014 |
| Citation | SIAM Journal on Matrix Analysis and Applications, 2014, v. 35, n. 3, p. 956-973 How to Cite? |
| Abstract | © 2014 Society for Industrial and Applied Mathematics. In this paper, we study the Birkhoff-von Neumann theorem for a class of multistochastic tensors. In particular, we give a necessary and sufficient condition such that a multistochastic tensor is a convex combination of finitely many permutation tensors. It is well-known that extreme points in the set of doubly stochastic matrices are just permutation matrices. However, we find that extreme points in the set of multistochastic tensors are not just permutation tensors. We provide the other types of tensors contained in the set of extreme points. |
| Persistent Identifier | http://hdl.handle.net/10722/277007 |
| ISSN | 2023 Impact Factor: 1.5 2023 SCImago Journal Rankings: 1.042 |
| ISI Accession Number ID |
| DC Field | Value | Language |
|---|---|---|
| dc.contributor.author | Cui, Lu Bin | - |
| dc.contributor.author | Li, Wen | - |
| dc.contributor.author | Ng, Michael K. | - |
| dc.date.accessioned | 2019-09-18T08:35:19Z | - |
| dc.date.available | 2019-09-18T08:35:19Z | - |
| dc.date.issued | 2014 | - |
| dc.identifier.citation | SIAM Journal on Matrix Analysis and Applications, 2014, v. 35, n. 3, p. 956-973 | - |
| dc.identifier.issn | 0895-4798 | - |
| dc.identifier.uri | http://hdl.handle.net/10722/277007 | - |
| dc.description.abstract | © 2014 Society for Industrial and Applied Mathematics. In this paper, we study the Birkhoff-von Neumann theorem for a class of multistochastic tensors. In particular, we give a necessary and sufficient condition such that a multistochastic tensor is a convex combination of finitely many permutation tensors. It is well-known that extreme points in the set of doubly stochastic matrices are just permutation matrices. However, we find that extreme points in the set of multistochastic tensors are not just permutation tensors. We provide the other types of tensors contained in the set of extreme points. | - |
| dc.language | eng | - |
| dc.relation.ispartof | SIAM Journal on Matrix Analysis and Applications | - |
| dc.subject | Multistochastic tensors | - |
| dc.subject | Permutation tensors | - |
| dc.subject | Permanent | - |
| dc.subject | Doubly stochastic matrices | - |
| dc.title | Birkhoff-von Neumann theorem for multistochastic tensors | - |
| dc.type | Article | - |
| dc.description.nature | link_to_subscribed_fulltext | - |
| dc.identifier.doi | 10.1137/120896499 | - |
| dc.identifier.scopus | eid_2-s2.0-84907809419 | - |
| dc.identifier.volume | 35 | - |
| dc.identifier.issue | 3 | - |
| dc.identifier.spage | 956 | - |
| dc.identifier.epage | 973 | - |
| dc.identifier.eissn | 1095-7162 | - |
| dc.identifier.isi | WOS:000343229800006 | - |
| dc.identifier.issnl | 0895-4798 | - |