A gradient system approach for Hankel structured low-rank approximation

Antonio Fazzi, Nicola Guglielmi, Ivan Markovsky

Research output: Contribution to journalArticle


Rank deficient Hankel matrices are at the core of several applications. However, in practice, the coefficients of these matrices are noisy due to e.g. measurements errors and computational errors, so generically the involved matrices are full rank. This motivates the problem of Hankel structured low-rank approximation. Structured low-rank approximation problems, in general, do not have a global and efficient solution technique. In this paper we propose a local optimization approach based on a two-levels iteration. Experimental results show that the proposed algorithm usually achieves good accuracy and shows a higher robustness with respect to the initial approximation, compared to alternative approaches.
Original languageEnglish
Pages (from-to)236-257
Number of pages22
JournalLinear Algebra & its Applications
Publication statusPublished - Aug 2021


  • Hankel matrix
  • Low-rank approximation
  • Gradient system
  • Structured matrix perturbation

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