Table of Links
Abstract and 1 Introduction
1.1 ESPRIT algorithm and central limit error scaling
1.2 Contribution
1.3 Related work
1.4 Technical overview and 1.5 Organization
2 Proof of the central limit error scaling
3 Proof of the optimal error scaling
4 Second-order eigenvector perturbation theory
5 Strong eigenvector comparison
5.1 Construction of the “good” P
5.2 Taylor expansion with respect to the error terms
5.3 Error cancellation in the Taylor expansion
5.4 Proof of Theorem 5.1
A Preliminaries
B Vandermonde matrice
C Deferred proofs for Section 2
D Deferred proofs for Section 4
E Deferred proofs for Section 5
F Lower bound for spectral estimation
References
F Lower bound for spectral estimation
To prove this theorem, we will employ the following lemma [AAL23, Thm. 1.8]:
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This paper is available on arxiv under CC BY 4.0 DEED license.
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Authors:
(1) Zhiyan Ding, Department of Mathematics, University of California, Berkeley;
(2) Ethan N. Epperly, Department of Computing and Mathematical Sciences, California Institute of Technology, Pasadena, CA, USA;
(3) Lin Lin, Department of Mathematics, University of California, Berkeley, Applied Mathematics and Computational Research Division, Lawrence Berkeley National Laboratory, and Challenge Institute for Quantum Computation, University of California, Berkeley;
(4) Ruizhe Zhang, Simons Institute for the Theory of Computing.
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