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

• Published in: Communications on pure and applied mathematics Vol. 70; no. 5; pp. 822 - 883
• Main Authors: Chen, Yuxin, Candès, Emmanuel J.
• Format: Journal Article
• Language: English
• Published: New York John Wiley and Sons, Limited 01.05.2017
• Subjects: Applied mathematics; Linear equations
• ISSN: 0010-3640; 1097-0312
• DOI: 10.1002/cpa.21638

We consider the fundamental problem of solving quadratic systems of equations in yi=|〈ai,x〉|2, i=1,…,m, and x∈ℝn is unknown. We propose a novel method, which starts with an initial guess computed by means of a spectral method and proceeds by minimizing a nonconvex functional as in the Wirtinger flow...