Solving Random Quadratic Systems of Equations Is Nearly as Easy as Solving Linear Systems

@article{Chen2015SolvingRQ,
  title={Solving Random Quadratic Systems of Equations Is Nearly as Easy as Solving Linear Systems},
  author={Y. Chen and E. Cand{\`e}s},
  journal={ArXiv},
  year={2015},
  volume={abs/1505.05114}
}
  • Y. Chen, E. Candès
  • Published 2015
  • Mathematics, Computer Science
  • ArXiv
  • We consider the fundamental problem of solving quadratic systems of equations in $n$ variables, where $y_i = |\langle \boldsymbol{a}_i, \boldsymbol{x} \rangle|^2$, $i = 1, \ldots, m$ and $\boldsymbol{x} \in \mathbb{R}^n$ is unknown. We propose a novel method, which starting with an initial guess computed by means of a spectral method, proceeds by minimizing a nonconvex functional as in the Wirtinger flow approach. There are several key distinguishing features, most notably, a distinct objective… CONTINUE READING
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