The local convexity of solving systems of quadratic equations

R Ward
R Ward
CD White
CD White

Results in Mathematics, pp. 569-608, 2017.

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Abstract:

This paper considers the recovery of a rank r positive semidefinite matrix \({X X^T \in \mathbb{R}^{n\times n}}\) from m scalar measurements of the form \({y_i := a_i^T X X^T a_i}\) (i.e., quadratic measurements of X). Such problems arise in a variety of applications, including covariance sketching of high-dimensional data streams, quadra...More

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