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

@inproceedings{Chen2015SolvingRQ,
  title={Solving Random Quadratic Systems of Equations Is Nearly as Easy as Solving Linear Systems},
  author={Yuxin Chen and Emmanuel J. Cand{\`e}s},
  booktitle={NIPS},
  year={2015}
}
We consider the fundamental problem of solving quadratic systems of equations in n variables, where yi = |〈ai,x〉|, i = 1, . . . ,m and x ∈ R 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 [11]. There are several key distinguishing features, most notably, a distinct objective functional and novel update rules, which operate in an adaptive fashion… CONTINUE READING
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Supplemental materials for: “solving random quadratic systems of equations is nearly as easy as solving linear systems

Y. Chen, E. J. Candès
2015
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