WorldCat Identities

Klep, Igor

Overview
Works: 156 works in 188 publications in 3 languages and 538 library holdings
Roles: Author, Thesis advisor, Reviewer, Other, htt
Classifications: QA188, 512.9434
Publication Timeline
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Most widely held works by Igor Klep
Optimization of polynomials in non-commuting variables by Sabine Burgdorf( )

12 editions published in 2016 in English and held by 274 WorldCat member libraries worldwide

This 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
Dilations, linear matrix inequalities, the matrix cube problem and beta distributions by J. William Helton( Book )

4 editions published in 2019 in English and Undetermined and held by 32 WorldCat member libraries worldwide

An operator C on a Hilbert space \mathcal H dilates to an operator T on a Hilbert space \mathcal K if there is an isometry V:\mathcal H\to \mathcal K such that C= V^* TV. A main result of this paper is, for a positive integer d, the simultaneous dilation, up to a sharp factor \vartheta (d), expressed as a ratio of \Gamma functions for d even, of all d\times d symmetric matrices of operator norm at most one to a collection of commuting self-adjoint contraction operators on a Hilbert space
Infeasibility certificates for linear matrix inequalities by Igor Klep( )

4 editions published in 2011 in English and German and held by 22 WorldCat member libraries worldwide

Semidefinitno programiranje in njegova uporaba by Janez Povh( Book )

1 edition published in 2011 in Slovenian and held by 13 WorldCat member libraries worldwide

Zbirka nalog iz matematike II by Kristijan Cafuta( Book )

1 edition published in 2018 in Slovenian and held by 7 WorldCat member libraries worldwide

Geometry of free loci and factorization of noncommutative polynomials by J. William Helton( Book )

2 editions published in 2017 in English and held by 6 WorldCat member libraries worldwide

Sums of hermitian squares and the BMV conjecture by Igor Klep( )

4 editions published between 2008 and 2011 in English and held by 4 WorldCat member libraries worldwide

Realni spekter nekomutativnega kolobarja in vložitve urejenih in [zvezdica]-urejenih celih kolobarjev v obsege : doktorska disertacija by Igor Klep( Book )

1 edition published in 2006 in Slovenian and held by 4 WorldCat member libraries worldwide

V komutativni realni algebri je osrednje orodje realni spekter komutativnega kolobarja, ki ga definiramo kot množico ekvivalentnih razredov homomorfizmov iz danega kolobarja v linearno urejene komutativne obsege ali celostna polja opremljeno s primerno topologijo. V nekomutativni realni algebri imamo opravka z nekomutativnimi asociativnimi kolobarji, zato se ukvarjamo s homomorfizmi v linearno urejene obsege in cele kolobarje. To nam porodi dve definiciji realnega spektra nekomutativnega kolobarja, ki si ju ogledamo v prvem poglavju. Zraven definicije matričnega realnega spektra je glavni rezultat prvega poglavja še nekomutativna različica Artin-Langovega izreka o homomorfizmu. Matrični realni spekter kolobarja $A$ je množica ekvivalenčnih razredov homomorfizmov iz $A$ v linearno urejene obsege, zato se pojavi vprašanje obstoja vložitve linearno urejenega celega kolobarja v (linearno urejene) obsege. S tem se ukvarjamo v 2. poglavju. V prvi polovici poglavja si ogledamo različice klasičnih, Orejevih vložitvenih izrekov. Pri tem dokažemo, da lahko linearne ureditve razširjamo na Orejeve lokalizacije po regularnih elementih. Druga polovica poglavja je namenjena vložitvenim izrekom, za katere potrebujemo teorijo valuacij in topološke metode. Dokažemo,da lahko vsak linearno urejen kolobar z diskretno usklajeno valuacijo, katere prirejeni stopničast kolobar je Orejev, vložimo v linearno urejen obseg. V drugi polovici doktorske disertacije se ukvarjamo z $\ast$-ureditvami in $\ast$-valuacijami. Za kolobar ali obseg z involucijo definiramo $\ast$-ureditev kot linearno ureditev Jordanove algebre simetričnih elementov, ki je invariantna za $\ast$-konjugiranje. V začetku 3. poglavja se ukvarjamo z $\ast$-urejenimi obsegi, ponovimo nekaj znanih izrekov in izpeljemo nove rezultate, predvsem iz teorije valuacij $\ast$-urejenih obsegov. Dokažemo tudi $\ast$-različico Neumannovega izreka. V drugi polovici poglavja se osredotočimo na cele $\ast$-kolobarje z $\ast$-ureditvami in pripadajočo teorijo valuacij. Podamo tudi več zgledov uporabe izpeljane teorije. Kompleksno grupno algebro lahko vselej opremimo z involucijo, ki element grupe pošlje v njegov inverz. Če ima takšna grupna algebra kakšno $\ast$-ureditev, potem grupo imenujemo $\ast$-uredljiva. Z razredom le-teh se ukvarjamo v zadnjem poglavju. Pokažemo, da je ta razred elementaren in celo kvazivarieteta. Dokažemo tudi, da je vsaka $\ast$-uredljiva grupa linearno uredljiva, ne pa tudi obratno
Connes' embedding conjectures and sums of hermitian squares by Igor Klep( )

2 editions published between 2008 and 2011 in English and held by 3 WorldCat member libraries worldwide

A Nichtnegativstellensatz for polynomials in noncommuting variables by Igor Klep( )

2 editions published between 2007 and 2011 in English and held by 3 WorldCat member libraries worldwide

Realna algebraična geometrija s poudarkom na realni algebri in pozitivnih polinomih by Igor Klep( Book )

1 edition published in 2011 in Slovenian and held by 3 WorldCat member libraries worldwide

Trace-positive polynomials and the quartic tracial moment problem by Sabine Burgdorf( )

1 edition published in 2010 in English and held by 2 WorldCat member libraries worldwide

The tracial moment problem and trace-optimization of polynomials by Sabine Burgdorf( Book )

2 editions published in 2011 in English and held by 2 WorldCat member libraries worldwide

Free analysis, convexity and LMI domains by J. William Helton( Book )

2 editions published in 2011 in English and held by 2 WorldCat member libraries worldwide

<> by Michael Jury( )

1 edition published in 2020 in English and held by 2 WorldCat member libraries worldwide

Vsote hermitskih kvadratov nekomutativnih polinomov : doktorska disertacija by Kristijan Cafuta( Book )

1 edition published in 2013 in Slovenian and held by 2 WorldCat member libraries worldwide

V disertaciji se ukvarjamo z realnimi polinomi v nekomutirajočih spremenljivkah. Zanimajo nas različne ideje pozitivnosti; pozitivnost preko pozitivne semidefinitnosti in pozitivnost sledi. Obe pozitivnosti definiramo in študiramo s pomočjo vsot hermitskih kvadratov (in komutatorjev) ter semidefinitnega programiranja. Prikažemo, da je obstoj razcepa na vsoto hermitskih kvadratov (in komutatorjev) ekvivalenten dopustnosti ustreznega semidefinitnega programa. S to metodo pokažemo, kako lahko poiščemo globalni minimum (lastnih vrednosti) simetričnega nk polinoma in hkrati določimo pripadajoče optimalne točke. V nadaljevanju si s pomočjo komutatorjev in ciklične ekvivalence ogledamo poenostavitev razreda nk polinomov z nenegativno sledjo. Predstavimo, kako (ob določeni predpostavki) poiščemo optimalne točke minimuma sledi danega nk polinoma. Del naloge namenimo študiranju matričnih algeber, prirejenih dobljenim semidefinitnim programom. Pokažemo, da so problemi vsote kvadratov in vsote hermitskih kvadratov najslabši možni. V primeru vsote hermitskih kvadratov in komutatorjev pa poiščemo primer, ko je situacija drugačna. V disertaciji se ukvarjamo tudi z optimizacijo nk polinomov na nk kocki oziroma nk krogli. Izkaže se, da ima vsak nk polinom, ki je pozitivno semidefiniten na nk krogli oziroma nk kocki, razcep na vsoto hermitskih kvadratov z utežmi. Razvito teorijo nato uporabimo za izračun minimuma in pripadajočih optimalnih točk danega nk polinoma na nk krogli oziroma nk kocki. Del disertacije je namenjen iskanju razcepa na vsoto hermitskih kvadratov in komutatorjev nk polinomov, ki se pojavijo pri reševanju BMV domneve. Delo zaključimo s prikazom implementacije algoritmov s primeri, podanimi v razvitem Matlab paketu \texttt {NCSOStools}
Extreme Points of Matrix Convex Sets, Free Spectrahedra, and Dilation Theory by Eric Evert( )

1 edition published in 2017 in English and held by 2 WorldCat member libraries worldwide

Infeasibility certificates for linear matrix inequalities by Igor Klep( Book )

2 editions published in 2011 in English and held by 2 WorldCat member libraries worldwide

The convex Positivstellensatz in a free algebra by J. William Helton( )

1 edition published in 2011 in English and held by 2 WorldCat member libraries worldwide

*-orderable semigroups by Igor Klep( )

1 edition published in 2009 in English and held by 2 WorldCat member libraries worldwide

 
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Optimization of polynomials in non-commuting variables
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Alternative Names
Igor Klep matamaiticeoir Slóivéanach

Igor Klep matemático esloveno

Igor Klep matemáticu eslovenu

Igor Klep matematikan slloven

Igor Klep Slovene mathematician

Igor Klep slovenski matematik

Igor Klep wiskundige uit Slovenië

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