The article rigorously discusses enhancements to the ESPRIT algorithm's error scaling in spectral estimation, emphasizing optimal performance under central limit conditions. Key insights include the novel use of matrix perturbation techniques and Vandermonde matrix properties to derive practical bounds on eigenvalue estimations. Comparison with previous results highlights significant improvements, with detailed proofs and technical discussions relegated to appendices. By refining established methodologies, this research sets a foundation for the advancement of spectral estimation techniques.
Our analysis demonstrates that the ESPRIT algorithm can achieve optimal error scaling under the central limit framework, refining previous assumptions and providing clear pathways for practical implementation.
In this study, we leverage advanced matrix perturbation techniques and Vandermonde matrix properties to explore the convergence behavior of eigenvalue estimations within the ESPRIT context.
Technical insights include leveraging Moitra's bounds and powerful bounding theorems to derive results that have significant implications for spectral estimation accuracy, significantly informing future work.
Our techniques not only build upon prior work but also enhance existing proofs by integrating new methods, leading to efficient error reduction in spectral estimation applications.
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