A global solution for the structured total least squares problem with block circulant matrices

Amir Beck, Aharon Ben-Tal

Research output: Contribution to journalArticlepeer-review

Abstract

We study the structured total least squares (STLS) problem of system of linear equations Ax = b, where A has a block circulant structure with N blocks. We show that by applying the discrete Fourier transform (DFT), the STLS problem decomposes into N unstructured total least squares (TLS) problems. The N solutions of these problems are then assembled to generate the optimal global solution of the STLS problem. Similar results are obtained for elementary block circulant matrices. Here the optimal solution is obtained by assembling two solutions: one of an unstructured TLS problem and the second of a multidimensional TLS problem.

Original languageEnglish
Pages (from-to)238-255
Number of pages18
JournalSIAM Journal on Matrix Analysis and Applications
Volume27
Issue number1
DOIs
StatePublished - 2006
Externally publishedYes

Keywords

  • Block circulant matrices
  • Discrete fourier transform
  • Structured total least squares

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