Exact Solutions in Structured Low-Rank Approximation

Giorgio Ottaviani (1) , Pierre-Jean Spaenlehauer (2) , Bernd Sturmfels (3)

1 Dipartimento di Matematica "Ulisse Dini"
2 CARAMEL - Cryptology, Arithmetic: Hardware and Software
3 Department of Mathematics [Berkeley]

Structured low-rank approximation is the problem of minimizing a weighted Frobenius distance to a given matrix among all matrices of fixed rank in a linear space of matrices. We study exact solutions to this problem by way of computational algebraic geometry. A particular focus lies on Hankel matrices, Sylvester matrices and generic linear spaces.

Domaines: Calcul formel [cs.SC]; Optimisation et contrôle [math.OC]; Géométrie algébrique [math.AG]; Calcul [stat.CO]

Giorgio Ottaviani, Pierre-Jean Spaenlehauer, Bernd Sturmfels. Exact Solutions in Structured Low-Rank Approximation. SIAM Journal on Matrix Analysis and Applications, 2014, 35, 4, pp.1521-1542. ⟨10.1137/13094520X⟩. ⟨hal-00953702⟩