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 the critical pointsof this optimization problem using algebraic geometry. A particular focus lies on Hankel matrices, Sylvester matrices and generic linear spaces.
Exact solutions in structured low-rank approximation / Giorgio Ottaviani; Pierre-Jean Spaenlehauer; Bernd Sturmfels. - In: SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS. - ISSN 0895-4798. - STAMPA. - 35:(2014), pp. 1521-1542. [10.1137/13094520X]
Exact solutions in structured low-rank approximation
OTTAVIANI, GIORGIO MARIA;
2014
Abstract
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 the critical pointsof this optimization problem using algebraic geometry. A particular focus lies on Hankel matrices, Sylvester matrices and generic linear spaces.
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