Eigenvector Phase Retrieval: Recovering eigenvectors from the absolute value of their entries
Publication
, Journal Article
Steinerberger, S; Wu, HT
Published in: Linear Algebra and Its Applications
November 1, 2022
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.
Duke Scholars
Published In
Linear Algebra and Its Applications
DOI
ISSN
0024-3795
Publication Date
November 1, 2022
Volume
652
Start / End Page
239 / 252
Related Subject Headings
- Numerical & Computational Mathematics
- 49 Mathematical sciences
- 40 Engineering
- 09 Engineering
- 08 Information and Computing Sciences
- 01 Mathematical Sciences
Citation
APA
Chicago
ICMJE
MLA
NLM
Steinerberger, S., & Wu, H. T. (2022). Eigenvector Phase Retrieval: Recovering eigenvectors from the absolute value of their entries. Linear Algebra and Its Applications, 652, 239–252. https://doi.org/10.1016/j.laa.2022.08.002
Steinerberger, S., and H. T. Wu. “Eigenvector Phase Retrieval: Recovering eigenvectors from the absolute value of their entries.” Linear Algebra and Its Applications 652 (November 1, 2022): 239–52. https://doi.org/10.1016/j.laa.2022.08.002.
Steinerberger S, Wu HT. Eigenvector Phase Retrieval: Recovering eigenvectors from the absolute value of their entries. Linear Algebra and Its Applications. 2022 Nov 1;652:239–52.
Steinerberger, S., and H. T. Wu. “Eigenvector Phase Retrieval: Recovering eigenvectors from the absolute value of their entries.” Linear Algebra and Its Applications, vol. 652, Nov. 2022, pp. 239–52. Scopus, doi:10.1016/j.laa.2022.08.002.
Steinerberger S, Wu HT. Eigenvector Phase Retrieval: Recovering eigenvectors from the absolute value of their entries. Linear Algebra and Its Applications. 2022 Nov 1;652:239–252.
Published In
Linear Algebra and Its Applications
DOI
ISSN
0024-3795
Publication Date
November 1, 2022
Volume
652
Start / End Page
239 / 252
Related Subject Headings
- Numerical & Computational Mathematics
- 49 Mathematical sciences
- 40 Engineering
- 09 Engineering
- 08 Information and Computing Sciences
- 01 Mathematical Sciences