A generalized flat extension theorem for moment matrices

DOI10.1007/s00013-009-0007-6zbMath1183.30030OpenAlexW2145828587MaRDI QIDQ1039946

Monique Laurent, Mourrain, Bernard

Publication date: 23 November 2009

Published in: Archiv der Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00013-009-0007-6

zbMATH Keywords

Hankel operatormoment matrixpolynomial optimizationtruncated moment problem

Mathematics Subject Classification ID

Polynomials in real and complex fields: location of zeros (algebraic theorems) (12D10) Moment problems and interpolation problems in the complex plane (30E05)

Related Items

Polynomial-exponential decomposition from moments, On the construction of general cubature formula by flat extensions, Flat extension and ideal projection, Certifying the global optimality of quartic minimization over the sphere, Symmetric tensor decomposition, Prony's method on the sphere, The multidimensional truncated moment problem: the moment cone, The operator approach to the truncated multidimensional moment problem, A comparison of different notions of ranks of symmetric tensors, Border basis relaxation for polynomial optimization, Dimensional stability in truncated moment problems, The \(\mathcal A\)-truncated \(K\)-moment problem, Lasserre Hierarchy for Large Scale Polynomial Optimization in Real and Complex Variables, An idempotent approach to truncated moment problems, Prony's method in several variables, Sparse polynomial interpolation: sparse recovery, super-resolution, or Prony?, Prony's method under an almost sharp multivariate Ingham inequality, The multidimensional truncated moment problem: Carathéodory numbers from Hilbert functions, The Approach of Moments for Polynomial Equations, Flat extensions in ∗-algebras

Uses Software

• GloptiPoly

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A prolongation-projection algorithm for computing the finite real variety of an ideal
• Semidefinite characterization and computation of zero-dimensional real radical ideals
• The multidimensional moment problem
• Exponentially bounded positive definite functions
• Positive definite functions on Abelian semigroups
• Moment matrices, border bases and real radical computation
• Multivariate polynomials, duality, and structured matrices
• Global Optimization with Polynomials and the Problem of Moments
• Solving the truncated moment problem solves the full moment problem
• Flat extensions of positive moment matrices: recursively generated relations
• Detecting Global Optimality and Extracting Solutions in GloptiPoly
• Solution of the truncated complex moment problem for flat data
• Semidefinite Programming
• The truncated complex $K$-moment problem
• Revisiting two theorems of Curto and Fialkow on moment matrices