On the complex least squares problem with constrained phase
On the complex least squares problem with constrained phase
The problem of solving approximately in the least squares sense an overdetermined linear system of equations with complex valued coefficients is considered, where the elements of the solution vector are constrained to have the same phase. A direct solution to this problem is given in [Linear Algebra and Its Applications, Vol. 433, pp. 1719-1721]. An alternative direct solution that reduces the problem to a generalized eigenvalue problem is derived in this paper. The new solution is related to generalized low-rank matrix approximation and makes possible one to use existing robust and efficient algorithms.
Linear system of equations, Phase constraint, Low-rank approximation, Total least squares
987-992
Markovsky, Ivan
7d632d37-2100-41be-a4ff-90b92752212c
June 2011
Markovsky, Ivan
7d632d37-2100-41be-a4ff-90b92752212c
Markovsky, Ivan
(2011)
On the complex least squares problem with constrained phase.
SIAM Journal on Matrix Analysis and Applications, 32 (3), .
Abstract
The problem of solving approximately in the least squares sense an overdetermined linear system of equations with complex valued coefficients is considered, where the elements of the solution vector are constrained to have the same phase. A direct solution to this problem is given in [Linear Algebra and Its Applications, Vol. 433, pp. 1719-1721]. An alternative direct solution that reduces the problem to a generalized eigenvalue problem is derived in this paper. The new solution is related to generalized low-rank matrix approximation and makes possible one to use existing robust and efficient algorithms.
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Published date: June 2011
Keywords:
Linear system of equations, Phase constraint, Low-rank approximation, Total least squares
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Southampton Wireless Group
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Local EPrints ID: 272534
URI: http://eprints.soton.ac.uk/id/eprint/272534
PURE UUID: 5b9511d6-4202-4107-9934-087d849b28c8
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Date deposited: 29 Jun 2011 15:24
Last modified: 14 Mar 2024 10:04
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Author:
Ivan Markovsky
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