Mathematik und Statistikhttp://kops.uni-konstanz.de:80/handle/123456789/392020-11-24T01:46:51Z2020-11-24T01:46:51ZUncertainty and stochastic optimization : numerical methods, regularization and asymptotic analysisEckstein, Stephanpop233432123456789/518962020-11-23T11:56:28Z2020Uncertainty and stochastic optimization : numerical methods, regularization and asymptotic analysis
Eckstein, Stephan
2020Eckstein, Stephan510DOCTORAL_THESISurn:nbn:de:bsz:352-2-7eh1yhnujte03eng2020-11-23T12:40:08+01:00123456789/392020-11-23T11:40:08ZVerallgemeinerte thermoelastische Plattengleichungen : Wohlgestelltheit und SpektralanalyseFischer, Lisapop260039123456789/518702020-11-19T02:02:52Z2020Verallgemeinerte thermoelastische Plattengleichungen : Wohlgestelltheit und Spektralanalyse
Fischer, Lisa
2020Fischer, Lisa510DOCTORAL_THESISurn:nbn:de:bsz:352-2-iyxa6r0v9vpo2deu2020-11-18T12:50:59+01:00123456789/392020-11-18T11:50:59ZPolyhedral faces in Gram spectrahedra of binary formsMayer, Thorstenpop238877123456789/517262020-11-11T08:14:38Z2021Polyhedral faces in Gram spectrahedra of binary forms
Mayer, Thorsten
The positive semidefinite Gram matrices of a form f with real coefficients parametrize the sum-of-squares representations of f. The convex body formed by the entirety of these matrices is the so-called Gram spectrahedron of f. We analyze the facial structures of symmetric and Hermitian Gram spectrahedra in the case of binary forms. We give upper bounds for the dimensions of polyhedral faces in Hermitian Gram spectrahedra and show that, if the form f is sufficiently generic, they can be realized by faces that are simplices and whose extreme points are rank-one tensors. We use our construction to prove a similar statement for the real symmetric case.
2021Mayer, Thorsten510The positive semidefinite Gram matrices of a form f with real coefficients parametrize the sum-of-squares representations of f. The convex body formed by the entirety of these matrices is the so-called Gram spectrahedron of f. We analyze the facial structures of symmetric and Hermitian Gram spectrahedra in the case of binary forms. We give upper bounds for the dimensions of polyhedral faces in Hermitian Gram spectrahedra and show that, if the form f is sufficiently generic, they can be realized by faces that are simplices and whose extreme points are rank-one tensors. We use our construction to prove a similar statement for the real symmetric case.ElsevierJOURNAL_ARTICLEeng10.1016/j.laa.2020.08.0250024-37951873-1856133157608Linear Algebra and Its Applications2020-11-11T09:14:38+01:00123456789/39Linear Algebra and Its Applications ; 608 (2021). - S. 133-157. - Elsevier. - ISSN 0024-3795. - eISSN 1873-1856true2020-11-11T08:14:38ZSums of squares on reducible real curvesPlaumann, Danielpop93081123456789/515982020-11-03T07:46:08Z2010-08Sums of squares on reducible real curves
Plaumann, Daniel
We ask whether every polynomial function that is non-negative on a real algebraic curve can be expressed as a sum of squares in the coordinate ring. Scheiderer has classified all irreducible curves for which this is the case. For reducible curves, we show how the answer depends on the configuration of the irreducible components and give complete necessary and sufficient conditions. We also prove partial results in the more general case of finitely generated preorderings and discuss applications to the moment problem for semialgebraic sets.
2010-08Plaumann, Daniel510We ask whether every polynomial function that is non-negative on a real algebraic curve can be expressed as a sum of squares in the coordinate ring. Scheiderer has classified all irreducible curves for which this is the case. For reducible curves, we show how the answer depends on the configuration of the irreducible components and give complete necessary and sufficient conditions. We also prove partial results in the more general case of finitely generated preorderings and discuss applications to the moment problem for semialgebraic sets.SpringerJOURNAL_ARTICLEeng10.1007/s00209-009-0541-80025-58741432-18237777972654Mathematische Zeitschrift2020-11-03T08:46:08+01:00123456789/39Mathematische Zeitschrift ; 265 (2010), 4. - S. 777-797. - Springer. - ISSN 0025-5874. - eISSN 1432-1823true2020-11-03T07:46:08Z