The Pythagoras number of real sum of squares polynomials and sum of square magnitudes of polynomials

DOI10.1007/s10092-012-0068-yzbMath1334.11025OpenAlexW2141375841MaRDI QIDQ385438

Marc Van Barel, Thanh Hieu Le, Laurent Sorber

Publication date: 2 December 2013

Published in: Calcolo (Search for Journal in Brave)

Full work available at URL: https://lirias.kuleuven.be/handle/123456789/353291

zbMATH Keywords

Pythagoras numberlow-rank representationsum of square magnitudes of polynomialssum of squares polynomials

Mathematics Subject Classification ID

Related Items (4)

On bounds of the Pythagoras number of the sum of square magnitudes of Laurent polynomials ⋮ On generic and maximal \(k\)-ranks of binary forms ⋮ Algebraic stories from one and from the other pockets ⋮ An algorithm for decomposing a non-negative polynomial as a sum of squares of rational functions

Uses Software

• Complex Optimization Toolbox

Cites Work

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• Factorization of multivariate positive Laurent polynomials
• The extension problem for positive-definite functions
• On the Rank of Extreme Matrices in Semidefinite Programs and the Multiplicity of Optimal Eigenvalues
• Spectral Factorizations and Sums of Squares Representations via Semidefinite Programming
• The Pythagoras number of some affine algebras and local algebras.
• Unconstrained Optimization of Real Functions in Complex Variables

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