Magnitude least-squares fitting via semidefinite programming with applications to beamforming and multidimensional filter design

@article{Kassakian2005MagnitudeLF,
  title={Magnitude least-squares fitting via semidefinite programming with applications to beamforming and multidimensional filter design},
  author={Peter Kassakian},
  journal={Proceedings. (ICASSP '05). IEEE International Conference on Acoustics, Speech, and Signal Processing, 2005.},
  year={2005},
  volume={3},
  pages={iii/53-iii/56 Vol. 3}
}
The standard least-squares problem seeks to find a linear combination of columns of a given matrix that best approximates a target vector in Euclidean norm. The problem of finding a linear combination of columns, the componentwise magnitude of which approximates a target, is not a convex problem, but can be well-approximated using semidefinite programming. High quality solutions can be found by reformulating the problem as a generalization of a graph partitioning problem, relaxing a rank… CONTINUE READING
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