Exact Solutions in Structured Low-Rank Approximation

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 points of this optimization problem using algebraic geometry. A particular focus lies on Hankel matrices, Sylvester matrices and generic linear spaces.

DOI: 10.1137/13094520X

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Cite this paper

@article{Ottaviani2014ExactSI, title={Exact Solutions in Structured Low-Rank Approximation}, author={Giorgio Ottaviani and Pierre-Jean Spaenlehauer and Bernd Sturmfels}, journal={SIAM J. Matrix Analysis Applications}, year={2014}, volume={35}, pages={1521-1542} }