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

Amir Beck; Aharon Ben-Tal

doi:10.1137/040612233

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

Amir Beck, Aharon Ben-Tal

Research output: Contribution to journal › Article › peer-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 language	English
Pages (from-to)	238-255
Number of pages	18
Journal	SIAM Journal on Matrix Analysis and Applications
Volume	27
Issue number	1
DOIs	https://doi.org/10.1137/040612233
State	Published - 2006
Externally published	Yes

Keywords

Block circulant matrices
Discrete fourier transform
Structured total least squares

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10.1137/040612233

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

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Keywords

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