The article explores error scaling in the ESPRIT algorithm, analyzing optimal error rates and providing proofs for various theoretical concepts. It emphasizes the importance of eigenvector perturbation theory and offers explicit formulas and bounds for higher-order terms in the perturbation series. Additionally, it details the application of Schur polynomials and cofactor expansions in establishing formal results in this context. The technical sections are supplemented with proofs aimed at validating the overarching claims, ensuring rigor in the presented findings.
In Appendix D.1, we develop explicit formulations for higher-order terms in perturbation expansion, alongside constraints that are essential for bounding those terms effectively.
We leverage the properties of Schur polynomials to manage higher-order terms, utilizing the standard cofactor expansion for determinants to govern the expressions involved.
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