Exact Solutions in Structured Low-Rank Approximation

22 Feb 2017 · Ottaviani Giorgio, Spaenlehauer Pierre-Jean, Sturmfels Bernd ·

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.