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010   $a3-319-33338-0
024 7 $a10.1007/978-3-319-33338-0
035   $a(CKB)3710000000726843
035   $a(DE-He213)978-3-319-33338-0
035   $a(MiAaPQ)EBC4543269
035   $a(PPN)194379914
035   $a(EXLCZ)993710000000726843
100   $a20160607d2016      u|         0
101 0 $aeng
135   $aurnn#008mamaa
181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 10$aOptimization of Polynomials in Non-Commuting Variables /$fby Sabine Burgdorf, Igor Klep, Janez Povh
205   $a1st ed. 2016.
210  1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2016.
215   $a1 online resource (XV, 104 p. 2 illus. in color.)
225 1 $aSpringerBriefs in Mathematics,$x2191-8198
311   $a3-319-33336-4 
320   $aIncludes bibliographical references at the end of each chapters and index.
330   $aThis book presents recent results on positivity and optimization of polynomials in non-commuting variables. Researchers in non-commutative algebraic geometry, control theory, system engineering, optimization, quantum physics and information science will find the unified notation and mixture of algebraic geometry and mathematical programming useful. Theoretical results are matched with algorithmic considerations; several examples and information on how to use NCSOStools open source package to obtain the results provided. Results are presented on detecting the eigenvalue and trace positivity of polynomials in non-commuting variables using Newton chip method and Newton cyclic chip method, relaxations for constrained and unconstrained optimization problems, semidefinite programming formulations of the relaxations and finite convergence of the hierarchies of these relaxations, and the practical efficiency of algorithms.
410  0$aSpringerBriefs in Mathematics,$x2191-8198
606   $aGeometry, Algebraic
606   $aQuantum computers
606   $aOperations research
606   $aManagement science
606   $aComputer software
606   $aSystem theory
606   $aAlgebraic Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M11019
606   $aQuantum Computing$3https://scigraph.springernature.com/ontologies/product-market-codes/M14070
606   $aOperations Research, Management Science$3https://scigraph.springernature.com/ontologies/product-market-codes/M26024
606   $aMathematical Software$3https://scigraph.springernature.com/ontologies/product-market-codes/M14042
606   $aSystems Theory, Control$3https://scigraph.springernature.com/ontologies/product-market-codes/M13070
615  0$aGeometry, Algebraic.
615  0$aQuantum computers.
615  0$aOperations research.
615  0$aManagement science.
615  0$aComputer software.
615  0$aSystem theory.
615 14$aAlgebraic Geometry.
615 24$aQuantum Computing.
615 24$aOperations Research, Management Science.
615 24$aMathematical Software.
615 24$aSystems Theory, Control.
676   $a519.3
700   $aBurgdorf$b Sabine$4aut$4http://id.loc.gov/vocabulary/relators/aut$0756027
702   $aKlep$b Igor$4aut$4http://id.loc.gov/vocabulary/relators/aut
702   $aPovh$b Janez$4aut$4http://id.loc.gov/vocabulary/relators/aut
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910254085403321
996   $aOptimization of Polynomials in Non-Commuting Variables$92129510
997   $aUNINA