Publications [#365617] of Hau-Tieng Wu

Papers Published

1. Steinerberger, S; Wu, HT, Eigenvector Phase Retrieval: Recovering eigenvectors from the absolute value of their entries, Linear Algebra and Its Applications, vol. 652 (November, 2022), pp. 239-252 [doi]
   (last updated on 2024/04/19)

   Abstract:
   We consider the eigenvalue problem Ax=λx where A∈Rn×n and the eigenvalue is also real λ∈R. If we are given A, λ and, additionally, the absolute value of the entries of x (the vector (|xi|)i=1n), is there a fast way to recover x? In particular, can this be done quicker than computing x from scratch? This may be understood as a special case of the phase retrieval problem. We present a randomized algorithm which provably converges in expectation whenever λ is a simple eigenvalue. The problem should become easier when |λ| is large and we discuss another algorithm for that case as well.